Dolbeault, Jean Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results. (English) Zbl 1481.35006 Milan J. Math. 89, No. 2, 355-386 (2021). MSC: 35-02 35A23 26D10 35B06 35J60 35K55 46B70 46E35 49J40 49K20 49K30 53C21 PDFBibTeX XMLCite \textit{J. Dolbeault}, Milan J. Math. 89, No. 2, 355--386 (2021; Zbl 1481.35006) Full Text: DOI arXiv
Dolbeault, Jean; Zhang, An Flows and functional inequalities for fractional operators. (English) Zbl 1499.35629 Appl. Anal. 96, No. 9, 1547-1560 (2017). MSC: 35R11 26A33 35A23 35B33 35B40 35K65 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{A. Zhang}, Appl. Anal. 96, No. 9, 1547--1560 (2017; Zbl 1499.35629) Full Text: DOI arXiv
Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno Weighted fast diffusion equations II: sharp asymptotic rates of convergence in relative error by entropy methods. (English) Zbl 1361.35076 Kinet. Relat. Models 10, No. 1, 61-91 (2017). MSC: 35K55 35B40 49K30 26D10 35B06 46E35 49K20 35J20 PDFBibTeX XMLCite \textit{M. Bonforte} et al., Kinet. Relat. Models 10, No. 1, 61--91 (2017; Zbl 1361.35076) Full Text: DOI arXiv
Dolbeault, Jean; Esteban, Maria J.; Loss, Michael Interpolation inequalities, nonlinear flows, boundary terms, optimality and linearization. (English) Zbl 1386.35174 J. Elliptic Parabol. Equ. 2, No. 1-2, 267-295 (2016). MSC: 35K55 35B06 49K30 35J60 35J20 PDFBibTeX XMLCite \textit{J. Dolbeault} et al., J. Elliptic Parabol. Equ. 2, No. 1--2, 267--295 (2016; Zbl 1386.35174) Full Text: DOI arXiv
Dolbeault, Jean; Toscani, Giuseppe Best matching Barenblatt profiles are delayed. (English) Zbl 1311.35132 J. Phys. A, Math. Theor. 48, No. 6, Article ID 065206, 14 p. (2015). MSC: 35K65 05C70 28D20 60G18 35C06 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{G. Toscani}, J. Phys. A, Math. Theor. 48, No. 6, Article ID 065206, 14 p. (2015; Zbl 1311.35132) Full Text: DOI arXiv
Dolbeault, Jean; Toscani, Giuseppe Improved interpolation inequalities, relative entropy and fast diffusion equations. (English) Zbl 1450.46020 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 5, 917-934 (2013). MSC: 46E35 26D10 35K55 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{G. Toscani}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 5, 917--934 (2013; Zbl 1450.46020) Full Text: DOI arXiv
Dolbeault, Jean; Toscani, Giuseppe Fast diffusion equations: matching large time asymptotics by relative entropy methods. (English) Zbl 1252.35065 Kinet. Relat. Models 4, No. 3, 701-716 (2011). MSC: 35B40 39B62 35C20 35K65 35K59 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{G. Toscani}, Kinet. Relat. Models 4, No. 3, 701--716 (2011; Zbl 1252.35065) Full Text: DOI arXiv
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
Dolbeault, Jean; Gentil, Ivan; Guillin, Arnaud; Wang, Feng-Yu \(L^q\)-functional inequalities and weighted porous media equations. (English) Zbl 1148.26018 Potential Anal. 28, No. 1, 35-59 (2008). Reviewer: Wei Nian Li (Binzhou) MSC: 26D10 35K55 39B62 46E27 46E35 60E15 PDFBibTeX XMLCite \textit{J. Dolbeault} et al., Potential Anal. 28, No. 1, 35--59 (2008; Zbl 1148.26018) Full Text: DOI arXiv
Bartier, Jean-Philippe; Dolbeault, Jean; Illner, Reinhard; Kowalczyk, Michał A qualitative study of linear drift-diffusion equations with time-dependent or degenerate coefficients. (English) Zbl 1117.35030 Math. Models Methods Appl. Sci. 17, No. 3, 327-362 (2007). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35K10 26D10 35K15 35K20 35K65 46E35 47J20 PDFBibTeX XMLCite \textit{J.-P. Bartier} et al., Math. Models Methods Appl. Sci. 17, No. 3, 327--362 (2007; Zbl 1117.35030) Full Text: DOI
Blanchet, Adrien; Dolbeault, Jean; Perthame, Benoit Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions. (English) Zbl 1112.35023 Electron. J. Differ. Equ. 2006, Paper No. 44, 33 p. (2006). MSC: 35B40 35B45 35B30 35D05 35K15 35D10 35K60 92C17 PDFBibTeX XMLCite \textit{A. Blanchet} et al., Electron. J. Differ. Equ. 2006, Paper No. 44, 33 p. (2006; Zbl 1112.35023) Full Text: EuDML EMIS
Dolbeault, Jean; Karch, Grzegorz Large time behaviour of solutions to nonhomogeneous diffusion equations. (English) Zbl 1124.35011 Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 133-147 (2006). Reviewer: Vladimir N. Grebenev (Novosibirsk) MSC: 35B40 35K65 35E05 76S05 76R50 35K15 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{G. Karch}, Banach Cent. Publ. 74, 133--147 (2006; Zbl 1124.35011)
Dolbeault, J.; Felmer, P.; Loss, M.; Paturel, E. Lieb–Thirring type inequalities and Gagliardo–Nirenberg inequalities for systems. (English) Zbl 1104.35021 J. Funct. Anal. 238, No. 1, 193-220 (2006). Reviewer: Georgi E. Karadzhov (Sofia) MSC: 35P20 26D10 47F05 35J10 PDFBibTeX XMLCite \textit{J. Dolbeault} et al., J. Funct. Anal. 238, No. 1, 193--220 (2006; Zbl 1104.35021) Full Text: DOI arXiv
Dolbeault, Jean; Sánchez, Óscar; Soler, Juan Asymptotic behaviour for the Vlasov-Poisson system in the stellar-dynamics case. (English) Zbl 1057.70009 Arch. Ration. Mech. Anal. 171, No. 3, 301-327 (2004). MSC: 70F15 85A05 35Q72 PDFBibTeX XMLCite \textit{J. Dolbeault} et al., Arch. Ration. Mech. Anal. 171, No. 3, 301--327 (2004; Zbl 1057.70009) Full Text: DOI Link
Dolbeault, J.; Rein, G. Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics. (English) Zbl 1012.82024 Math. Models Methods Appl. Sci. 11, No. 3, 407-432 (2001). MSC: 82D10 35A22 35Q35 35Q40 35Q55 82C40 PDFBibTeX XMLCite \textit{J. Dolbeault} and \textit{G. Rein}, Math. Models Methods Appl. Sci. 11, No. 3, 407--432 (2001; Zbl 1012.82024) Full Text: DOI arXiv
Dolbeault, J. Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states). (English) Zbl 1115.82316 J. Math. Pures Appl. (9) 78, No. 2, 121-157 (1999). MSC: 82B40 35B45 35J05 PDFBibTeX XMLCite \textit{J. Dolbeault}, J. Math. Pures Appl. (9) 78, No. 2, 121--157 (1999; Zbl 1115.82316) Full Text: DOI