Abatangelo, Nicola; Gómez-Castro, David; Vázquez, Juan Luis Singular boundary behaviour and large solutions for fractional elliptic equations. (English) Zbl 1521.35181 J. Lond. Math. Soc., II. Ser. 107, No. 2, 568-615 (2023). MSC: 35R11 35D30 35J08 35J25 35R09 PDFBibTeX XMLCite \textit{N. Abatangelo} et al., J. Lond. Math. Soc., II. Ser. 107, No. 2, 568--615 (2023; Zbl 1521.35181) Full Text: DOI arXiv
Feo, Filomena; Vázquez, Juan Luis; Volzone, Bruno Anisotropic fast diffusion equations. (English) Zbl 1518.35186 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 233, Article ID 113298, 43 p. (2023). MSC: 35C06 35A08 35B40 35K15 35K59 35K65 PDFBibTeX XMLCite \textit{F. Feo} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 233, Article ID 113298, 43 p. (2023; Zbl 1518.35186) Full Text: DOI arXiv
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen R.; Vázquez, Juan Luis Evolution driven by the infinity fractional Laplacian. (English) Zbl 1520.35161 Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 136, 30 p. (2023). Reviewer: Peter Lindqvist (Trondheim) MSC: 35R11 35K55 35A01 PDFBibTeX XMLCite \textit{F. del Teso} et al., Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 136, 30 p. (2023; Zbl 1520.35161) Full Text: DOI arXiv
Vázquez, Juan Luis A survey on mass conservation and related topics in nonlinear diffusion. arXiv:2311.18357 Preprint, arXiv:2311.18357 [math.AP] (2023). MSC: 35R11 35K55 35K65 35C06 35A08 35B40 BibTeX Cite \textit{J. L. Vázquez}, ``A survey on mass conservation and related topics in nonlinear diffusion'', Preprint, arXiv:2311.18357 [math.AP] (2023) Full Text: arXiv OA License
Vázquez, Juan Luis The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences. arXiv:2310.20569 Preprint, arXiv:2310.20569 [math.AP] (2023). MSC: 35K55 35K65 35A08 35B40 BibTeX Cite \textit{J. L. Vázquez}, ``The very singular solution for the Anisotropic Fast Diffusion Equation and its consequences'', Preprint, arXiv:2310.20569 [math.AP] (2023) Full Text: arXiv OA License
Vázquez, Juan Luis Asymptotic behaviour for the heat equation in hyperbolic space. (English) Zbl 1528.35219 Commun. Anal. Geom. 30, No. 9, 2123-2156 (2022). Reviewer: Ti-Jun Xiao (Fudan) MSC: 35R01 35B40 35K05 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Commun. Anal. Geom. 30, No. 9, 2123--2156 (2022; Zbl 1528.35219) Full Text: DOI arXiv
Carrillo, José A.; Gómez-Castro, David; Vázquez, Juan Luis A fast regularisation of a Newtonian vortex equation. (English) Zbl 1510.35180 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 3, 705-747 (2022). MSC: 35L65 35D40 65M25 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 39, No. 3, 705--747 (2022; Zbl 1510.35180) Full Text: DOI arXiv
Chan, Hardy; Gómez-Castro, David; Vázquez, Juan Luis Singular solutions for fractional parabolic boundary value problems. (English) Zbl 1498.35567 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 4, Paper No. 159, 38 p. (2022). MSC: 35R11 35C15 35D30 35K08 35K20 35K67 35S16 PDFBibTeX XMLCite \textit{H. Chan} et al., Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 4, Paper No. 159, 38 p. (2022; Zbl 1498.35567) Full Text: DOI arXiv
Carrillo, J. A.; Gómez-Castro, D.; Vázquez, J. L. Vortex formation for a non-local interaction model with Newtonian repulsion and superlinear mobility. (English) Zbl 1484.35283 Adv. Nonlinear Anal. 11, 937-967 (2022). MSC: 35L65 35L60 35L45 35L67 35D40 65M25 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Adv. Nonlinear Anal. 11, 937--967 (2022; Zbl 1484.35283) Full Text: DOI arXiv
Carrillo, Jose A.; Gómez-Castro, David; Vázquez, Juan Luis Infinite-time concentration in aggregation-diffusion equations with a given potential. (English. French summary) Zbl 1481.35048 J. Math. Pures Appl. (9) 157, 346-398 (2022). MSC: 35B40 35B44 35D40 35K15 35K59 35K65 35Q84 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., J. Math. Pures Appl. (9) 157, 346--398 (2022; Zbl 1481.35048) Full Text: DOI arXiv
Vázquez, Juan Luis Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range. (English) Zbl 1476.35320 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112575, 35 p. (2022). MSC: 35R11 35B45 35C06 35K92 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112575, 35 p. (2022; Zbl 1476.35320) Full Text: DOI arXiv
del Teso, Félix; Endal, Jørgen; Vázquez, Juan Luis The one-phase fractional Stefan problem. (English) Zbl 1473.80010 Math. Models Methods Appl. Sci. 31, No. 1, 83-131 (2021). MSC: 80A22 35D30 35K15 35K65 35R09 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{F. del Teso} et al., Math. Models Methods Appl. Sci. 31, No. 1, 83--131 (2021; Zbl 1473.80010) Full Text: DOI arXiv
Feo, Filomena; Vázquez, Juan Luis; Volzone, Bruno Anisotropic \(p\)-Laplacian evolution of fast diffusion type. (English) Zbl 1472.35234 Adv. Nonlinear Stud. 21, No. 3, 523-555 (2021). MSC: 35K92 35K65 35A08 35B40 PDFBibTeX XMLCite \textit{F. Feo} et al., Adv. Nonlinear Stud. 21, No. 3, 523--555 (2021; Zbl 1472.35234) Full Text: DOI arXiv
Vázquez, Juan Luis The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case. (English) Zbl 1471.35312 Calc. Var. Partial Differ. Equ. 60, No. 4, Paper No. 140, 59 p. (2021). MSC: 35R11 35K15 35K92 35K65 35A08 35B06 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Calc. Var. Partial Differ. Equ. 60, No. 4, Paper No. 140, 59 p. (2021; Zbl 1471.35312) Full Text: DOI arXiv Backlinks: MO
Chan, Hardy; Gómez-Castro, David; Vázquez, Juan Luis Blow-up phenomena in nonlocal eigenvalue problems: when theories of \(L^1\) and \(L^2\) meet. (English) Zbl 1458.35070 J. Funct. Anal. 280, No. 7, Article ID 108845, 69 p. (2021). MSC: 35B44 35R09 35R11 35J25 35B50 35D30 45C05 PDFBibTeX XMLCite \textit{H. Chan} et al., J. Funct. Anal. 280, No. 7, Article ID 108845, 69 p. (2021; Zbl 1458.35070) Full Text: DOI arXiv
Parviainen, Mikko; Vázquez, Juan Luis Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications. (English) Zbl 1476.35130 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 21, Spec. Iss., 303-359 (2020). Reviewer: Peter Lindqvist (Trondheim) MSC: 35K92 35K55 35B40 35D40 35K59 35K20 35B07 PDFBibTeX XMLCite \textit{M. Parviainen} and \textit{J. L. Vázquez}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 21, 303--359 (2020; Zbl 1476.35130) Full Text: DOI arXiv
Vázquez, J. L. The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour. (English) Zbl 1447.35205 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 199, Article ID 112034, 31 p. (2020). MSC: 35K92 35K65 35R11 35A08 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 199, Article ID 112034, 31 p. (2020; Zbl 1447.35205) Full Text: DOI arXiv
Álvarez, Gabriel; Martínez Alonso, Luis; Medina, Elena; Vázquez, Juan Luis Separatrices in the Hamilton-Jacobi formalism of inflaton models. (English) Zbl 1446.83008 J. Math. Phys. 61, No. 4, 043501, 18 p. (2020). MSC: 83F05 83C15 70H20 37C70 PDFBibTeX XMLCite \textit{G. Álvarez} et al., J. Math. Phys. 61, No. 4, 043501, 18 p. (2020; Zbl 1446.83008) Full Text: DOI arXiv
Audrito, Alessandro; Vázquez, Juan Luis Travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains. (English) Zbl 1439.35257 J. Differ. Equations 269, No. 3, 2664-2696 (2020). Reviewer: Vincenzo Vespri (Firenze) MSC: 35K57 35K65 35C07 35K55 PDFBibTeX XMLCite \textit{A. Audrito} and \textit{J. L. Vázquez}, J. Differ. Equations 269, No. 3, 2664--2696 (2020; Zbl 1439.35257) Full Text: DOI arXiv
del Teso, Félix; Endal, Jørgen; Vázquez, Juan Luis On the two-phase fractional Stefan problem. (English) Zbl 1434.80006 Adv. Nonlinear Stud. 20, No. 2, 437-458 (2020). MSC: 80A22 35D30 35K15 35K65 35R09 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{F. del Teso} et al., Adv. Nonlinear Stud. 20, No. 2, 437--458 (2020; Zbl 1434.80006) Full Text: DOI arXiv
Segatti, Antonio; Vázquez, Juan Luis On a fractional thin film equation. (English) Zbl 1437.35429 Adv. Nonlinear Anal. 9, 1516-1558 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 35K55 35R11 35C06 35D30 35Q35 PDFBibTeX XMLCite \textit{A. Segatti} and \textit{J. L. Vázquez}, Adv. Nonlinear Anal. 9, 1516--1558 (2020; Zbl 1437.35429) Full Text: DOI arXiv
Gómez-Castro, David; Vázquez, Juan Luis The fractional Schrödinger equation with singular potential and measure data. (English) Zbl 1425.35212 Discrete Contin. Dyn. Syst. 39, No. 12, 7113-7139 (2019). MSC: 35R11 35J10 35D30 35J67 35J75 PDFBibTeX XMLCite \textit{D. Gómez-Castro} and \textit{J. L. Vázquez}, Discrete Contin. Dyn. Syst. 39, No. 12, 7113--7139 (2019; Zbl 1425.35212) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Existence of weak solutions for a general porous medium equation with nonlocal pressure. (English) Zbl 1437.35430 Arch. Ration. Mech. Anal. 233, No. 1, 451-496 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35K55 35Q35 35R11 35D30 35B45 PDFBibTeX XMLCite \textit{D. Stan} et al., Arch. Ration. Mech. Anal. 233, No. 1, 451--496 (2019; Zbl 1437.35430) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Porous medium equation with nonlocal pressure. (English) Zbl 1406.35302 Rassias, Themistocles M. (ed.), Current research in nonlinear analysis. In honor of Haim Brezis and Louis Nirenberg. Cham: Springer (ISBN 978-3-319-89799-8/hbk; 978-3-319-89800-1/ebook). Springer Optimization and Its Applications 135, 277-308 (2018). MSC: 35Q35 35K35 76S05 35A01 35A02 35B40 35C06 PDFBibTeX XMLCite \textit{D. Stan} et al., Springer Optim. Appl. 135, 277--308 (2018; Zbl 1406.35302) Full Text: DOI arXiv
Díaz, J. I.; Gómez-Castro, D.; Vázquez, J. L. The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach. (English) Zbl 1402.35093 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 177, Part A, 325-360 (2018). MSC: 35J10 35D30 35J67 35J75 35R11 PDFBibTeX XMLCite \textit{J. I. Díaz} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 177, Part A, 325--360 (2018; Zbl 1402.35093) Full Text: DOI arXiv
Vázquez, Juan Luis Asymptotic behaviour for the fractional heat equation in the Euclidean space. (English) Zbl 1388.35216 Complex Var. Elliptic Equ. 63, No. 7-8, 1216-1231 (2018). MSC: 35R11 35K55 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Complex Var. Elliptic Equ. 63, No. 7--8, 1216--1231 (2018; Zbl 1388.35216) Full Text: DOI arXiv
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations. (English) Zbl 1392.35144 Calc. Var. Partial Differ. Equ. 57, No. 2, Paper No. 57, 34 p. (2018). MSC: 35J61 35J25 35J40 35B09 35B45 35B65 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Calc. Var. Partial Differ. Equ. 57, No. 2, Paper No. 57, 34 p. (2018; Zbl 1392.35144) Full Text: DOI arXiv
Kienzler, Clemens; Koch, Herbert; Vázquez, Juan Luis Flatness implies smoothness for solutions of the porous medium equation. (English) Zbl 1403.35065 Calc. Var. Partial Differ. Equ. 57, No. 1, Paper No. 18, 42 p. (2018). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B65 35B45 35K55 35K65 76S99 35R35 PDFBibTeX XMLCite \textit{C. Kienzler} et al., Calc. Var. Partial Differ. Equ. 57, No. 1, Paper No. 18, 42 p. (2018; Zbl 1403.35065) Full Text: DOI arXiv
Bonforte, Matteo; Figalli, Alessio; Vázquez, Juan Luis Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains. (English) Zbl 1443.35067 Anal. PDE 11, No. 4, 945-982 (2018). Reviewer: Vincenzo Vespri (Firenze) MSC: 35K55 35K65 35B45 35B65 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Anal. PDE 11, No. 4, 945--982 (2018; Zbl 1443.35067) Full Text: DOI arXiv Link
Audrito, Alessandro; Vázquez, Juan Luis The Fisher-KPP problem with doubly nonlinear diffusion. (English) Zbl 1386.35197 J. Differ. Equations 263, No. 11, 7647-7708 (2017). MSC: 35K57 35K65 35C07 35K55 PDFBibTeX XMLCite \textit{A. Audrito} and \textit{J. L. Vázquez}, J. Differ. Equations 263, No. 11, 7647--7708 (2017; Zbl 1386.35197) Full Text: DOI arXiv
Vázquez, Juan Luis; de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana Classical solutions and higher regularity for nonlinear fractional diffusion equations. (English) Zbl 1371.35331 J. Eur. Math. Soc. (JEMS) 19, No. 7, 1949-1975 (2017). MSC: 35R11 35S10 35B65 35K55 PDFBibTeX XMLCite \textit{J. L. Vázquez} et al., J. Eur. Math. Soc. (JEMS) 19, No. 7, 1949--1975 (2017; Zbl 1371.35331) Full Text: DOI arXiv
Audrito, Alessandro; Vázquez, Juan Luis The Fisher-KPP problem with doubly nonlinear “fast” diffusion. (English) Zbl 1365.35065 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 157, 212-248 (2017). MSC: 35K57 35K65 35C07 35K55 PDFBibTeX XMLCite \textit{A. Audrito} and \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 157, 212--248 (2017; Zbl 1365.35065) Full Text: DOI arXiv
Grillo, Gabriele; Muratori, Matteo; Vázquez, Juan Luis The porous medium equation on Riemannian manifolds with negative curvature. the large-time behaviour. (English) Zbl 1437.35428 Adv. Math. 314, 328-377 (2017). Reviewer: Vincenzo Vespri (Firenze) MSC: 35K55 35B40 35K65 58J35 PDFBibTeX XMLCite \textit{G. Grillo} et al., Adv. Math. 314, 328--377 (2017; Zbl 1437.35428) Full Text: DOI arXiv
Vázquez, Juan Luis Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D. (English) Zbl 1360.35089 J. Evol. Equ. 16, No. 3, 723-758 (2016). MSC: 35K55 35K65 35S10 35R11 76S05 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Evol. Equ. 16, No. 3, 723--758 (2016; Zbl 1360.35089) Full Text: DOI arXiv
Vázquez, Juan Luis The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation. (English) Zbl 1348.35042 J. Differ. Equations 260, No. 7, 6038-6056 (2016). Reviewer: Vladimir N. Grebenev (Darmstadt) MSC: 35B45 35B65 35K55 35K65 35R11 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Differ. Equations 260, No. 7, 6038--6056 (2016; Zbl 1348.35042) Full Text: DOI arXiv
Bonforte, Matteo; Vázquez, Juan Luis Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. (English) Zbl 1328.35009 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 131, 363-398 (2016). MSC: 35B45 35B65 35K55 35K65 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 131, 363--398 (2016; Zbl 1328.35009) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Finite and infinite speed of propagation for porous medium equations with nonlocal pressure. (English) Zbl 1379.35253 J. Differ. Equations 260, No. 2, 1154-1199 (2016). MSC: 35Q35 35K65 76S05 35R11 PDFBibTeX XMLCite \textit{D. Stan} et al., J. Differ. Equations 260, No. 2, 1154--1199 (2016; Zbl 1379.35253) Full Text: DOI arXiv
Grillo, Gabriele; Muratori, Matteo; Vázquez, Juan Luis The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour. arXiv:1604.06126 Preprint, arXiv:1604.06126 [math.AP] (2016). MSC: 35B40 35K55 35K65 BibTeX Cite \textit{G. Grillo} et al., ``The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour'', Preprint, arXiv:1604.06126 [math.AP] (2016) Full Text: arXiv OA License
Bonforte, Matteo; Sire, Yannick; Vázquez, Juan Luis Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. (English) Zbl 1347.35129 Discrete Contin. Dyn. Syst. 35, No. 12, 5725-5767 (2015). Reviewer: Vladimir N. Grebenev (Darmstadt) MSC: 35K55 35K61 35K65 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Discrete Contin. Dyn. Syst. 35, No. 12, 5725--5767 (2015; Zbl 1347.35129) Full Text: DOI arXiv
Vázquez, Juan Luis The mesa problem for the fractional porous medium equation. (English) Zbl 1327.35214 Interfaces Free Bound. 17, No. 2, 261-286 (2015). Reviewer: Piotr Biler (Wroclaw) MSC: 35K65 35S10 26A33 35C06 35J87 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Interfaces Free Bound. 17, No. 2, 261--286 (2015; Zbl 1327.35214) Full Text: DOI arXiv
Bonforte, Matteo; Vázquez, Juan Luis A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains. (English) Zbl 1334.35382 Arch. Ration. Mech. Anal. 218, No. 1, 317-362 (2015). Reviewer: Daniel Spector (Hsinchu City) MSC: 35R11 35D30 35B45 26A33 76S05 80A20 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vázquez}, Arch. Ration. Mech. Anal. 218, No. 1, 317--362 (2015; Zbl 1334.35382) Full Text: DOI arXiv
Vázquez, Juan Luis Fundamental solution and long time behavior of the porous medium equation in hyperbolic space. (English. French summary) Zbl 1327.35213 J. Math. Pures Appl. (9) 104, No. 3, 454-484 (2015). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35K65 58J35 35K55 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Math. Pures Appl. (9) 104, No. 3, 454--484 (2015; Zbl 1327.35213) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Transformations of self-similar solutions for porous medium equations of fractional type. (English) Zbl 1383.35248 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 119, 62-73 (2015). MSC: 35R11 35C06 35K65 76S05 PDFBibTeX XMLCite \textit{D. Stan} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 119, 62--73 (2015; Zbl 1383.35248) Full Text: DOI arXiv
Vázquez, Juan Luis Progress in the theory of nonlinear diffusion: asymptotics via entropy methods. (English) Zbl 1327.35171 Ancona, Vincenzo (ed.) et al., Trends in contemporary mathematics. Selected talks based on the presentations at the INdAM day, June 18, 2014. Cham: Springer (ISBN 978-3-319-05253-3/hbk; 978-3-319-05254-0/ebook). Springer INdAM Series 8, 105-124 (2014). MSC: 35K55 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Springer INdAM Ser. 8, 105--124 (2014; Zbl 1327.35171) Full Text: DOI
Stan, Diana; Vázquez, Juan Luis The Fisher-KPP equation with nonlinear fractional diffusion. (English) Zbl 1323.35088 SIAM J. Math. Anal. 46, No. 5, 3241-3276 (2014). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35K57 26A33 35K65 76S05 35C06 35C07 PDFBibTeX XMLCite \textit{D. Stan} and \textit{J. L. Vázquez}, SIAM J. Math. Anal. 46, No. 5, 3241--3276 (2014; Zbl 1323.35088) Full Text: DOI arXiv Link
Perthame, Benoît; Quirós, Fernando; Vázquez, Juan Luis The Hele-Shaw asymptotics for mechanical models of tumor growth. (English) Zbl 1293.35347 Arch. Ration. Mech. Anal. 212, No. 1, 93-127 (2014). MSC: 35Q92 92C50 76D27 92D25 35B40 PDFBibTeX XMLCite \textit{B. Perthame} et al., Arch. Ration. Mech. Anal. 212, No. 1, 93--127 (2014; Zbl 1293.35347) Full Text: DOI arXiv
Vázquez, Juan Luis Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type. (English) Zbl 1297.35279 J. Eur. Math. Soc. (JEMS) 16, No. 4, 769-803 (2014). Reviewer: Juan J. Trujillo (La Laguna) MSC: 35R11 35A08 35B40 35K65 76S05 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Eur. Math. Soc. (JEMS) 16, No. 4, 769--803 (2014; Zbl 1297.35279) Full Text: DOI arXiv
Bonforte, Matteo; Vázquez, Juan Luis Quantitative local and global a priori estimates for fractional nonlinear diffusion equations. (English) Zbl 1288.35127 Adv. Math. 250, 242-284 (2014). MSC: 35B45 35B65 35K55 35K65 35R11 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vázquez}, Adv. Math. 250, 242--284 (2014; Zbl 1288.35127) Full Text: DOI arXiv
Stan, Diana; del Teso, Félix; Vázquez, Juan Luis Finite and infinite speed of propagation for porous medium equations with fractional pressure. (Vitesse de propagation finie et infinie pour des équations du milieu poreux avec une pression fractionnaire.) (English. Abridged French version) Zbl 1284.35352 C. R., Math., Acad. Sci. Paris 352, No. 2, 123-128 (2014). MSC: 35Q35 76S05 35D30 35R11 76R50 PDFBibTeX XMLCite \textit{D. Stan} et al., C. R., Math., Acad. Sci. Paris 352, No. 2, 123--128 (2014; Zbl 1284.35352) Full Text: DOI arXiv
Portilheiro, Manuel; Vázquez, Juan Luis Degenerate homogeneous parabolic equations associated with the infinity-Laplacian. (English) Zbl 1262.35137 Calc. Var. Partial Differ. Equ. 46, No. 3-4, 705-724 (2013). MSC: 35K65 35K59 35B40 35D40 PDFBibTeX XMLCite \textit{M. Portilheiro} and \textit{J. L. Vázquez}, Calc. Var. Partial Differ. Equ. 46, No. 3--4, 705--724 (2013; Zbl 1262.35137) Full Text: DOI arXiv
Bonforte, Matteo; Gazzola, Filippo; Grillo, Gabriele; Vázquez, Juan Luis Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space. (English) Zbl 1262.35109 Calc. Var. Partial Differ. Equ. 46, No. 1-2, 375-401 (2013). MSC: 35J61 35J15 35B40 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Calc. Var. Partial Differ. Equ. 46, No. 1--2, 375--401 (2013; Zbl 1262.35109) Full Text: DOI arXiv
Stan, Diana; Vázquez, Juan Luis Asymptotic behaviour of the doubly nonlinear diffusion equation \(u_t=\Delta_pu^m\) on bounded domains. (English) Zbl 1258.35130 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 77, 1-32 (2013). MSC: 35K65 35B40 35B45 35K55 35K92 35C06 35K20 PDFBibTeX XMLCite \textit{D. Stan} and \textit{J. L. Vázquez}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 77, 1--32 (2013; Zbl 1258.35130) Full Text: DOI arXiv
Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis Quantitative local bounds for subcritical semilinear elliptic equations. (English) Zbl 1261.35028 Milan J. Math. 80, No. 1, 65-118 (2012). MSC: 35B45 35B65 35J61 35B33 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Milan J. Math. 80, No. 1, 65--118 (2012; Zbl 1261.35028) Full Text: DOI arXiv
Fila, Marek; Vázquez, Juan Luis; Winkler, Michael; Yanagida, Eiji Rate of convergence to Barenblatt profiles for the fast diffusion equation. (English) Zbl 1315.76032 Arch. Ration. Mech. Anal. 204, No. 2, 599-625 (2012). MSC: 76R50 35Q35 PDFBibTeX XMLCite \textit{M. Fila} et al., Arch. Ration. Mech. Anal. 204, No. 2, 599--625 (2012; Zbl 1315.76032) Full Text: DOI arXiv
De Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana; Vázquez, Juan Luis A general fractional porous medium equation. (English) Zbl 1248.35220 Commun. Pure Appl. Math. 65, No. 9, 1242-1284 (2012). MSC: 35R11 35Q35 35D35 35A02 35B30 PDFBibTeX XMLCite \textit{A. De Pablo} et al., Commun. Pure Appl. Math. 65, No. 9, 1242--1284 (2012; Zbl 1248.35220) Full Text: DOI arXiv Link
Portilheiro, Manuel; Vázquez, Juan Luis A porous medium equation involving the infinity-Laplacian viscosity solutions and asymptotic behavior. (English) Zbl 1248.35113 Commun. Partial Differ. Equations 37, No. 4-6, 753-793 (2012). MSC: 35K92 35D40 35B40 35B50 35K65 35K67 35B09 35R35 35C06 76S05 PDFBibTeX XMLCite \textit{M. Portilheiro} and \textit{J. L. Vázquez}, Commun. Partial Differ. Equations 37, No. 4--6, 753--793 (2012; Zbl 1248.35113) Full Text: DOI arXiv
Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis Behaviour near extinction for the fast diffusion equation on bounded domains. (English) Zbl 1241.35013 J. Math. Pures Appl. (9) 97, No. 1, 1-38 (2012). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B33 35B40 46E35 35K20 35K65 PDFBibTeX XMLCite \textit{M. Bonforte} et al., J. Math. Pures Appl. (9) 97, No. 1, 1--38 (2012; Zbl 1241.35013) Full Text: DOI arXiv
Vázquez, Juan Luis; Winkler, Michael Highly time-oscillating solutions for very fast diffusion equations. (English) Zbl 1252.35168 J. Evol. Equ. 11, No. 3, 725-742 (2011). MSC: 35K65 35K59 35K20 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez} and \textit{M. Winkler}, J. Evol. Equ. 11, No. 3, 725--742 (2011; Zbl 1252.35168) Full Text: DOI
Fila, Marek; Vázquez, Juan-Luis; Winkler, Michael A continuum of extinction rates for the fast diffusion equation. (English) Zbl 1229.35124 Commun. Pure Appl. Anal. 10, No. 4, 1129-1147 (2011). MSC: 35K65 35B40 PDFBibTeX XMLCite \textit{M. Fila} et al., Commun. Pure Appl. Anal. 10, No. 4, 1129--1147 (2011; Zbl 1229.35124) Full Text: DOI arXiv
Vázquez, Juan Luis; Winkler, Michael The evolution of singularities in fast diffusion equations: infinite-time blow-down. (English) Zbl 1233.35131 SIAM J. Math. Anal. 43, No. 4, 1499-1535 (2011). Reviewer: Marek Fila (Bratislava) MSC: 35K65 35B40 35A20 35K59 PDFBibTeX XMLCite \textit{J. L. Vázquez} and \textit{M. Winkler}, SIAM J. Math. Anal. 43, No. 4, 1499--1535 (2011; Zbl 1233.35131) Full Text: DOI
Mizoguchi, Noriko; Quirós, Fernando; Vázquez, Juan Luis Multiple blow-up for a porous medium equation with reaction. (English) Zbl 1233.35049 Math. Ann. 350, No. 4, 801-827 (2011). Reviewer: Marek Fila (Bratislava) MSC: 35B44 35K65 35K15 35K59 PDFBibTeX XMLCite \textit{N. Mizoguchi} et al., Math. Ann. 350, No. 4, 801--827 (2011; Zbl 1233.35049) Full Text: DOI
Iagar, Razvan Gabriel; Laurençot, Philippe; Vázquez, Juan Luis Asymptotic behaviour of a nonlinear parabolic equation with gradient absorption and critical exponent. (English) Zbl 1227.35064 Interfaces Free Bound. 13, No. 2, 271-295 (2011). MSC: 35B40 35K65 35K92 49L25 35K15 35D40 PDFBibTeX XMLCite \textit{R. G. Iagar} et al., Interfaces Free Bound. 13, No. 2, 271--295 (2011; Zbl 1227.35064) Full Text: DOI arXiv
Caffarelli, Luis; Vázquez, Juan-Luis Asymptotic behaviour of a porous medium equation with fractional diffusion. (English) Zbl 1211.35043 Discrete Contin. Dyn. Syst. 29, No. 4, 1393-1404 (2011). MSC: 35B40 35K55 35K65 35J87 26A33 35R11 35C06 PDFBibTeX XMLCite \textit{L. Caffarelli} and \textit{J.-L. Vázquez}, Discrete Contin. Dyn. Syst. 29, No. 4, 1393--1404 (2011; Zbl 1211.35043) Full Text: DOI arXiv
Bonforte, Matteo; Grillo, Gabriele; Vázquez, Juan Luis Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold. (English) Zbl 1209.35069 Arch. Ration. Mech. Anal. 196, No. 2, 631-680 (2010). Reviewer: Marek Fila (Bratislava) MSC: 35K65 35B40 35B06 35B33 35Q84 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Arch. Ration. Mech. Anal. 196, No. 2, 631--680 (2010; Zbl 1209.35069) Full Text: DOI arXiv
Bonforte, Matteo; Iagar, Razvan Gabriel; Vázquez, Juan Luis Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation. (English) Zbl 1198.35136 Adv. Math. 224, No. 5, 2151-2215 (2010). Reviewer: Elvira Mascolo (Firenze) MSC: 35K92 35B35 35B65 35K65 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Adv. Math. 224, No. 5, 2151--2215 (2010; Zbl 1198.35136) Full Text: DOI arXiv
Kamin, Shoshana; Reyes, Guillermo; Vázquez, Juan Luis Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density. (English) Zbl 1196.35052 Discrete Contin. Dyn. Syst. 26, No. 2, 521-549 (2010). MSC: 35B40 35K15 35K65 35K59 PDFBibTeX XMLCite \textit{S. Kamin} et al., Discrete Contin. Dyn. Syst. 26, No. 2, 521--549 (2010; Zbl 1196.35052) Full Text: DOI
Iagar, Razvan Gabriel; Vázquez, Juan L. Anomalous large-time behaviour of the \(p\)-Laplacian flow in an exterior domain in low dimension. (English) Zbl 1185.35021 J. Eur. Math. Soc. (JEMS) 12, No. 1, 249-277 (2010). Reviewer: Peter Lindqvist (Trondheim) MSC: 35B40 35K65 35R35 PDFBibTeX XMLCite \textit{R. G. Iagar} and \textit{J. L. Vázquez}, J. Eur. Math. Soc. (JEMS) 12, No. 1, 249--277 (2010; Zbl 1185.35021) Full Text: DOI
Bonforte, Matteo; Vázquez, Juan Luis Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations. (English) Zbl 1184.35083 Adv. Math. 223, No. 2, 529-578 (2010). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B45 35B65 35K59 35K65 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vázquez}, Adv. Math. 223, No. 2, 529--578 (2010; Zbl 1184.35083) Full Text: DOI
Vázquez, Juan Luis; Vitillaro, Enzo On the Laplace equation with dynamical boundary conditions of reactive-diffusive type. (English) Zbl 1167.35019 J. Math. Anal. Appl. 354, No. 2, 674-688 (2009). MSC: 35J60 35J65 35B65 35A22 35C05 PDFBibTeX XMLCite \textit{J. L. Vázquez} and \textit{E. Vitillaro}, J. Math. Anal. Appl. 354, No. 2, 674--688 (2009; Zbl 1167.35019) Full Text: DOI
Droniou, Jérôme; Vázquez, Juan-Luis Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions. (English) Zbl 1167.35342 Calc. Var. Partial Differ. Equ. 34, No. 4, 413-434 (2009). MSC: 35J25 35D05 35B30 35K20 47B44 35B65 PDFBibTeX XMLCite \textit{J. Droniou} and \textit{J.-L. Vázquez}, Calc. Var. Partial Differ. Equ. 34, No. 4, 413--434 (2009; Zbl 1167.35342) Full Text: DOI
Blanchet, Adrien; Bonforte, Matteo; Dolbeault, Jean; Grillo, Gabriele; Vázquez, Juan Luis Asymptotics of the fast diffusion equation via entropy estimates. (English) Zbl 1178.35214 Arch. Ration. Mech. Anal. 191, No. 2, 347-385 (2009). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 35K65 35B40 35B45 35K15 35B30 35C05 35B33 PDFBibTeX XMLCite \textit{A. Blanchet} et al., Arch. Ration. Mech. Anal. 191, No. 2, 347--385 (2009; Zbl 1178.35214) Full Text: DOI arXiv Link
Iagar, Razvan Gabriel; Vázquez, Juan Luis Asymptotic analysis of the \(p\)-Laplacian flow in an exterior domain. (English) Zbl 1178.35070 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 2, 497-520 (2009). Reviewer: Peter Lindqvist (Trondheim) MSC: 35B40 35K65 35R35 35K20 35K55 PDFBibTeX XMLCite \textit{R. G. Iagar} and \textit{J. L. Vázquez}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 2, 497--520 (2009; Zbl 1178.35070) Full Text: DOI EuDML
Vázquez, Juan Luis Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion. (English) Zbl 1197.35153 J. Math. Anal. Appl. 352, No. 1, 515-547 (2009). Reviewer: Pavol Quittner (Bratislava) MSC: 35K65 53C44 35K55 35D30 35K59 35K15 PDFBibTeX XMLCite \textit{J. L. Vázquez}, J. Math. Anal. Appl. 352, No. 1, 515--547 (2009; Zbl 1197.35153) Full Text: DOI
Reyes, Guillermo; Vázquez, Juan-Luis Long time behavior for the inhomogeneous PME in a medium with slowly decaying density. (English) Zbl 1169.35313 Commun. Pure Appl. Anal. 8, No. 2, 493-508 (2009). MSC: 35B40 35K15 35K65 35K55 PDFBibTeX XMLCite \textit{G. Reyes} and \textit{J.-L. Vázquez}, Commun. Pure Appl. Anal. 8, No. 2, 493--508 (2009; Zbl 1169.35313) Full Text: DOI
Bonforte, Matteo; Grillo, Gabriele; Vazquez, Juan Luis Fast diffusion flow on manifolds of nonpositive curvature. (English) Zbl 1139.35065 J. Evol. Equ. 8, No. 1, 99-128 (2008). MSC: 35K65 35B45 35B65 35K55 58J35 PDFBibTeX XMLCite \textit{M. Bonforte} et al., J. Evol. Equ. 8, No. 1, 99--128 (2008; Zbl 1139.35065) Full Text: DOI Link
Iagar, Razvan Gabriel; Sánchez, Ariel; Vázquez, Juan Luis Radial equivalence for the two basic nonlinear degenerate diffusion equations. (English) Zbl 1139.35067 J. Math. Pures Appl. (9) 89, No. 1, 1-24 (2008). Reviewer: Peter Lindqvist (Trondheim) MSC: 35K65 35Q35 35K55 PDFBibTeX XMLCite \textit{R. G. Iagar} et al., J. Math. Pures Appl. (9) 89, No. 1, 1--24 (2008; Zbl 1139.35067) Full Text: DOI
Vázquez, Juan Luis Porous medium flow in a tube. Traveling waves and KPP behavior. (English) Zbl 1157.35061 Commun. Contemp. Math. 9, No. 5, 731-751 (2007). Reviewer: Mersaid Aripov (Tashkent) MSC: 35K65 35K55 35K20 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Commun. Contemp. Math. 9, No. 5, 731--751 (2007; Zbl 1157.35061) Full Text: DOI
Mannucci, Paola; Vazquez, Juan Luis Viscosity solutions for elliptics-parabolic problems. (English) Zbl 1141.35013 NoDEA, Nonlinear Differ. Equ. Appl. 14, No. 1-2, 75-90 (2007). MSC: 35D05 35K65 35R35 35K60 PDFBibTeX XMLCite \textit{P. Mannucci} and \textit{J. L. Vazquez}, NoDEA, Nonlinear Differ. Equ. Appl. 14, No. 1--2, 75--90 (2007; Zbl 1141.35013) Full Text: DOI
Bonforte, Matteo; Vazquez, Juan Luis Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations. (English) Zbl 1166.35008 Bound. Value Probl. 2007, Article ID 21425, 31 p. (2007). Reviewer: Elvira Mascolo (Firenze) MSC: 35B65 35K65 35K20 35B05 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vazquez}, Bound. Value Probl. 2007, Article ID 21425, 31 p. (2007; Zbl 1166.35008) Full Text: DOI arXiv EuDML
Brändle, Cristina; Quirós, Fernando; Vázquez, Juan Luis Asymptotic behaviour of the porous media equation in domains with holes. (English) Zbl 1131.35043 Interfaces Free Bound. 9, No. 2, 211-231 (2007). MSC: 35K65 35C20 35R35 PDFBibTeX XMLCite \textit{C. Brändle} et al., Interfaces Free Bound. 9, No. 2, 211--231 (2007; Zbl 1131.35043) Full Text: DOI
Laurençot, Philippe; Vázquez, Juan Luis Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption. (English) Zbl 1134.35070 J. Dyn. Differ. Equations 19, No. 4, 985-1005 (2007). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35K65 35B40 49L25 35K55 35B05 PDFBibTeX XMLCite \textit{P. Laurençot} and \textit{J. L. Vázquez}, J. Dyn. Differ. Equations 19, No. 4, 985--1005 (2007; Zbl 1134.35070) Full Text: DOI arXiv
Carrillo, J. A.; Vázquez, J. L. Asymptotic complexity in filtration equations. (English) Zbl 1156.35051 J. Evol. Equ. 7, No. 3, 471-495 (2007). Reviewer: Shigeru Sakaguchi (Hiroshima) MSC: 35K55 35B40 35K15 PDFBibTeX XMLCite \textit{J. A. Carrillo} and \textit{J. L. Vázquez}, J. Evol. Equ. 7, No. 3, 471--495 (2007; Zbl 1156.35051) Full Text: DOI
Vázquez, Juan Luis Perspectives in nonlinear diffusion: between analysis, physics and geometry. (English) Zbl 1128.35060 Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume I: Plenary lectures and ceremonies. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 609-634 (2007). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K65 35K55 35B40 35K15 PDFBibTeX XMLCite \textit{J. L. Vázquez}, in: Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22--30, 2006. Volume I: Plenary lectures and ceremonies. Zürich: European Mathematical Society (EMS). 609--634 (2007; Zbl 1128.35060)
Vázquez, Juan Luis The porous medium equation. Mathematical theory. (English) Zbl 1107.35003 Oxford Mathematical Monographs; Oxford Science Publications. Oxford: Oxford University Press (ISBN 0-19-856903-3/hbk). xxii, 624 p. (2007). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 35-02 35Kxx 35K65 76S05 PDFBibTeX XMLCite \textit{J. L. Vázquez}, The porous medium equation. Mathematical theory. Oxford: Oxford University Press (2007; Zbl 1107.35003)
Chasseigne, Emmanuel; Vasquez, Juan Luis Extended solutions for general fast diffusion equations with optimal measure data. (English) Zbl 1173.35561 Adv. Differ. Equ. 11, No. 6, 627-646 (2006). Reviewer: Pavol Quittner (Bratislava) MSC: 35K65 35K55 35K15 35B40 PDFBibTeX XMLCite \textit{E. Chasseigne} and \textit{J. L. Vasquez}, Adv. Differ. Equ. 11, No. 6, 627--646 (2006; Zbl 1173.35561)
Reyes, Guillermo; Vazquez, Juan Luis The Cauchy problem for the inhomogeneous porous medium equation. (English) Zbl 1124.35035 Netw. Heterog. Media 1, No. 2, 337-351 (2006). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 35K65 35K60 35B40 35D05 35K55 PDFBibTeX XMLCite \textit{G. Reyes} and \textit{J. L. Vazquez}, Netw. Heterog. Media 1, No. 2, 337--351 (2006; Zbl 1124.35035) Full Text: DOI
Reyes, Guillermo; Vásquez, Juan Luis A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media. (English) Zbl 1162.35033 J. Eur. Math. Soc. (JEMS) 8, No. 3, 531-554 (2006). Reviewer: Joachim Naumann (Berlin) MSC: 35J60 35K55 35K65 35B05 35B40 47H20 PDFBibTeX XMLCite \textit{G. Reyes} and \textit{J. L. Vásquez}, J. Eur. Math. Soc. (JEMS) 8, No. 3, 531--554 (2006; Zbl 1162.35033) Full Text: DOI
Souplet, Philippe; Vázquez, Juan Luis Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. (English) Zbl 1116.35070 Discrete Contin. Dyn. Syst. 14, No. 1, 221-234 (2006). Reviewer: Marek Fila (Bratislava) MSC: 35K60 35K55 35B40 PDFBibTeX XMLCite \textit{P. Souplet} and \textit{J. L. Vázquez}, Discrete Contin. Dyn. Syst. 14, No. 1, 221--234 (2006; Zbl 1116.35070) Full Text: DOI
Fila, Marek; Ninomiya, Hirokazu; Vázquez, Juan Luis Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. (English) Zbl 1120.35048 Discrete Contin. Dyn. Syst. 14, No. 1, 63-74 (2006). Reviewer: Chiu Yeung Chan (Lafayette) MSC: 35K50 35K57 35B40 PDFBibTeX XMLCite \textit{M. Fila} et al., Discrete Contin. Dyn. Syst. 14, No. 1, 63--74 (2006; Zbl 1120.35048) Full Text: DOI
Ferreira, Raúl; De Pablo, Arturo; Vazquez, Juan Luis Classification of blow-up with nonlinear diffusion and localized reaction. (English) Zbl 1110.35034 J. Differ. Equations 231, No. 1, 195-211 (2006). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 35K65 35K15 35B05 35B30 35B45 35B33 PDFBibTeX XMLCite \textit{R. Ferreira} et al., J. Differ. Equations 231, No. 1, 195--211 (2006; Zbl 1110.35034) Full Text: DOI Link
Bonforte, Matteo; Vazquez, Juan Luis Global positivity estimates and Harnack inequalities for the fast diffusion equation. (English) Zbl 1107.35063 J. Funct. Anal. 240, No. 2, 399-428 (2006). Reviewer: Lubomira Softova (Bari) MSC: 35K55 35B40 35K65 PDFBibTeX XMLCite \textit{M. Bonforte} and \textit{J. L. Vazquez}, J. Funct. Anal. 240, No. 2, 399--428 (2006; Zbl 1107.35063) Full Text: DOI
Lee, Ki-Ahm; Petrosyan, Arshak; Vázquez, Juan Luis Large-time geometric properties of solutions of the evolution \(p\)-Laplacian equation. (English) Zbl 1108.35097 J. Differ. Equations 229, No. 2, 389-411 (2006). Reviewer: Marek Fila (Bratislava) MSC: 35K65 35B40 35K55 35B05 PDFBibTeX XMLCite \textit{K.-A. Lee} et al., J. Differ. Equations 229, No. 2, 389--411 (2006; Zbl 1108.35097) Full Text: DOI
Vázquez, Juan Luis Smoothing and decay estimates for nonlinear diffusion equations. Equations of porous medium type. (English) Zbl 1113.35004 Oxford Lecture Series in Mathematics and its Applications 33. Oxford: Oxford University Press (ISBN 0-19-920297-4/hbk). xiii, 234 p. (2006). Reviewer: Chiu Yeung Chan (Lafayette) MSC: 35-02 35B05 35B40 35K55 35K65 47H20 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Smoothing and decay estimates for nonlinear diffusion equations. Equations of porous medium type. Oxford: Oxford University Press (2006; Zbl 1113.35004) Backlinks: MO
Vázquez, Juan Luis; Zuazua, Enrique Lack of collision in a simplified 1D model for fluid-solid interaction. (English) Zbl 1387.35634 Math. Models Methods Appl. Sci. 16, No. 5, 637-678 (2006). MSC: 35R35 76D03 74F10 35K15 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez} and \textit{E. Zuazua}, Math. Models Methods Appl. Sci. 16, No. 5, 637--678 (2006; Zbl 1387.35634) Full Text: DOI
de Pablo, A.; Ferreira, R.; Quirós, F.; Vázquez, J. L. Blow-up. The mathematical problem of blow-up of reaction-diffusion equations and systems. (Spanish) Zbl 1244.35074 Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 32, 75-111 (2005). MSC: 35K57 35B40 PDFBibTeX XMLCite \textit{A. de Pablo} et al., Bol. Soc. Esp. Mat. Apl., S\(\vec{\text{e}}\)MA 32, 75--111 (2005; Zbl 1244.35074)
Vázquez, Juan Luis Failure of the strong maximum principle in nonlinear diffusion. Existence of needles. (English) Zbl 1100.35021 Commun. Partial Differ. Equations 30, No. 9, 1263-1303 (2005). Reviewer: Hanna Marcinkowska (Wrocław) MSC: 35B50 35B05 35K55 35K65 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Commun. Partial Differ. Equations 30, No. 9, 1263--1303 (2005; Zbl 1100.35021) Full Text: DOI
Vázquez, J. L. The porous medium equation. New contractivity results. (English) Zbl 1147.35050 Bandle, Catherine (ed.) et al., Elliptic and parabolic problems. A special tribute to the work of Haim Brezis. Basel: Birkhäuser (ISBN 3-7643-7249-4/hbk). Progress in Nonlinear Differential Equations and their Applications 63, 433-451 (2005). Reviewer: Shigeru Sakaguchi (Ehime) MSC: 35K55 35K65 35B05 35B35 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Prog. Nonlinear Differ. Equ. Appl. 63, 433--451 (2005; Zbl 1147.35050)
Brändle, Cristina; Vázquez, Juan Luis Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type. (English) Zbl 1084.35033 Indiana Univ. Math. J. 54, No. 3, 817-860 (2005). MSC: 35K65 35K15 35D05 PDFBibTeX XMLCite \textit{C. Brändle} and \textit{J. L. Vázquez}, Indiana Univ. Math. J. 54, No. 3, 817--860 (2005; Zbl 1084.35033) Full Text: DOI Link
Vázquez, Juan Luis Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations. (English) Zbl 1085.35083 Adv. Nonlinear Stud. 5, No. 1, 87-131 (2005). Reviewer: Andrey E. Shishkov (Donetsk) MSC: 35K65 35J60 35B05 35B40 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Adv. Nonlinear Stud. 5, No. 1, 87--131 (2005; Zbl 1085.35083)
Vázquez, Juan Luis The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation. (English) Zbl 1162.35392 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 15, No. 3-4, 281-300 (2004). MSC: 35K55 35K57 35B40 35B60 PDFBibTeX XMLCite \textit{J. L. Vázquez}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 15, No. 3--4, 281--300 (2004; Zbl 1162.35392)