Fuest, Mario; Lankeit, Johannes; Tanaka, Yuya Critical mass phenomena in higher dimensional quasilinear Keller-Segel systems with indirect signal production. (English) Zbl 07784870 Math. Methods Appl. Sci. 46, No. 13, 14362-14378 (2023). MSC: 35B33 35B44 35K59 92C17 PDFBibTeX XMLCite \textit{M. Fuest} et al., Math. Methods Appl. Sci. 46, No. 13, 14362--14378 (2023; Zbl 07784870) Full Text: DOI arXiv OA License
Valencia-Guevara, Julio C.; Pérez, John; Abreu, Eduardo On the well-posedness via the JKO approach and a study of blow-up of solutions for a multispecies Keller-Segel chemotaxis system with no mass conservation. (English) Zbl 1522.35522 J. Math. Anal. Appl. 528, No. 2, Article ID 127602, 32 p. (2023). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35A15 35B40 35B44 PDFBibTeX XMLCite \textit{J. C. Valencia-Guevara} et al., J. Math. Anal. Appl. 528, No. 2, Article ID 127602, 32 p. (2023; Zbl 1522.35522) Full Text: DOI
Marinoschi, Gabriela A semigroup approach to a reaction-diffusion system with cross-diffusion. (English) Zbl 1510.35136 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 230, Article ID 113222, 29 p. (2023). MSC: 35K51 35K57 35K61 47H04 47H06 47H20 92C17 PDFBibTeX XMLCite \textit{G. Marinoschi}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 230, Article ID 113222, 29 p. (2023; Zbl 1510.35136) Full Text: DOI
Fritz, Marvin; Khristenko, Ustim; Wohlmuth, Barbara Equivalence between a time-fractional and an integer-order gradient flow: the memory effect reflected in the energy. (English) Zbl 1500.35294 Adv. Nonlinear Anal. 12, Article ID 20220262, 23 p. (2023). MSC: 35R11 35A01 35A02 35A35 35B38 35D30 35K25 PDFBibTeX XMLCite \textit{M. Fritz} et al., Adv. Nonlinear Anal. 12, Article ID 20220262, 23 p. (2023; Zbl 1500.35294) Full Text: DOI arXiv
Tu, Xinyu; Mu, Chunlai; Zheng, Pan On effects of the nonlinear signal production to the boundedness and finite-time blow-up in a flux-limited chemotaxis model. (English) Zbl 1491.35072 Math. Models Methods Appl. Sci. 32, No. 4, 647-711 (2022). MSC: 35B44 35K51 35K59 35K65 92C17 PDFBibTeX XMLCite \textit{X. Tu} et al., Math. Models Methods Appl. Sci. 32, No. 4, 647--711 (2022; Zbl 1491.35072) Full Text: DOI
Chen, Wenbin; Liu, Qianqian; Shen, Jie Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. (English) Zbl 1485.65102 Int. J. Numer. Anal. Model. 19, No. 2-3, 275-298 (2022). MSC: 65M60 65M12 65M15 35K61 35K55 92C17 PDFBibTeX XMLCite \textit{W. Chen} et al., Int. J. Numer. Anal. Model. 19, No. 2--3, 275--298 (2022; Zbl 1485.65102) Full Text: Link
Chiyo, Yutaro; Yokota, Tomomi Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system. (English) Zbl 1485.35072 Z. Angew. Math. Phys. 73, No. 2, Paper No. 61, 27 p. (2022). MSC: 35B44 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{Y. Chiyo} and \textit{T. Yokota}, Z. Angew. Math. Phys. 73, No. 2, Paper No. 61, 27 p. (2022; Zbl 1485.35072) Full Text: DOI arXiv
Ji, Shanming; Wang, Zhi-An; Xu, Tianyuan; Yin, Jingxue A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion. (English) Zbl 1471.35078 Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 178, 19 p. (2021). MSC: 35C07 35K40 35K65 35K57 92C17 PDFBibTeX XMLCite \textit{S. Ji} et al., Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 178, 19 p. (2021; Zbl 1471.35078) Full Text: DOI arXiv
Chalub, Fabio A. C. C.; Monsaingeon, Léonard; Ribeiro, Ana Margarida; Souza, Max O. Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective. (English) Zbl 1473.35590 Acta Appl. Math. 171, Paper No. 24, 51 p. (2021). MSC: 35Q92 60J25 92D15 92D25 58E30 PDFBibTeX XMLCite \textit{F. A. C. C. Chalub} et al., Acta Appl. Math. 171, Paper No. 24, 51 p. (2021; Zbl 1473.35590) Full Text: DOI arXiv
Ehrlacher, Virginie; Lombardi, Damiano; Mula, Olga; Vialard, François-Xavier Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces. (English) Zbl 1476.65267 ESAIM, Math. Model. Numer. Anal. 54, No. 6, 2159-2197 (2020). MSC: 65M70 65M06 65N35 65M12 65M22 65D40 PDFBibTeX XMLCite \textit{V. Ehrlacher} et al., ESAIM, Math. Model. Numer. Anal. 54, No. 6, 2159--2197 (2020; Zbl 1476.65267) Full Text: DOI arXiv
Chen, Lin; Kong, Fanze; Wang, Qi Stationary ring and concentric-ring solutions of the Keller-Segel model with quadratic diffusion. (English) Zbl 1454.35027 SIAM J. Math. Anal. 52, No. 5, 4565-4615 (2020). Reviewer: Neng Zhu (Nanchang) MSC: 35B36 35B40 35K57 35Q92 92C17 35K51 35B32 PDFBibTeX XMLCite \textit{L. Chen} et al., SIAM J. Math. Anal. 52, No. 5, 4565--4615 (2020; Zbl 1454.35027) Full Text: DOI arXiv
Carrillo, Jose A.; Chen, Xinfu; Wang, Qi; Wang, Zhian; Zhang, Lu Phase transitions and bump solutions of the Keller-Segel model with volume exclusion. (English) Zbl 1475.35036 SIAM J. Appl. Math. 80, No. 1, 232-261 (2020). Reviewer: Yuanyuan Ke (Beijing) MSC: 35B35 35B36 35B40 35J57 35K65 82C26 92C17 92D25 34B08 34B15 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., SIAM J. Appl. Math. 80, No. 1, 232--261 (2020; Zbl 1475.35036) Full Text: DOI arXiv
Karmakar, Debabrata; Wolansky, Gershon On Patlak-Keller-Segel system for several populations: a gradient flow approach. (English) Zbl 1422.35125 J. Differ. Equations 267, No. 12, 7483-7520 (2019). MSC: 35K65 35K40 35Q92 PDFBibTeX XMLCite \textit{D. Karmakar} and \textit{G. Wolansky}, J. Differ. Equations 267, No. 12, 7483--7520 (2019; Zbl 1422.35125) Full Text: DOI arXiv
Ferreira, L. C. F.; Santos, M. C.; Valencia-Guevara, J. C. Minimizing movement for a fractional porous medium equation in a periodic setting. (English) Zbl 1433.35185 Bull. Sci. Math. 153, 86-117 (2019). Reviewer: Mohammed Kaabar (Gelugor) MSC: 35K65 26A33 35K55 76S05 35K15 49Jxx 58Exx 28A33 PDFBibTeX XMLCite \textit{L. C. F. Ferreira} et al., Bull. Sci. Math. 153, 86--117 (2019; Zbl 1433.35185) Full Text: DOI arXiv
Matthes, Daniel; Plazotta, Simon A variational formulation of the BDF2 method for metric gradient flows. (English) Zbl 1416.65150 ESAIM, Math. Model. Numer. Anal. 53, No. 1, 145-172 (2019). MSC: 65J08 34G25 35A15 35G25 35K46 65L06 PDFBibTeX XMLCite \textit{D. Matthes} and \textit{S. Plazotta}, ESAIM, Math. Model. Numer. Anal. 53, No. 1, 145--172 (2019; Zbl 1416.65150) Full Text: DOI arXiv
Guo, Li; Li, Xingjie Helen; Yang, Yang Energy dissipative local discontinuous Galerkin methods for Keller-Segel chemotaxis model. (English) Zbl 1419.65061 J. Sci. Comput. 78, No. 3, 1387-1404 (2019). MSC: 65M60 65M20 65L06 35Q92 92C17 35B44 PDFBibTeX XMLCite \textit{L. Guo} et al., J. Sci. Comput. 78, No. 3, 1387--1404 (2019; Zbl 1419.65061) Full Text: DOI
Wang, Jinhuan; Li, Yue; Chen, Li Supercritical degenerate parabolic-parabolic Keller-Segel system: existence criterion given by the best constant in Sobolev’s inequality. (English) Zbl 1415.35159 Z. Angew. Math. Phys. 70, No. 3, Paper No. 71, 18 p. (2019). MSC: 35K55 35B44 PDFBibTeX XMLCite \textit{J. Wang} et al., Z. Angew. Math. Phys. 70, No. 3, Paper No. 71, 18 p. (2019; Zbl 1415.35159) Full Text: DOI arXiv
Plazotta, Simon A BDF2-approach for the non-linear Fokker-Planck equation. (English) Zbl 1417.35202 Discrete Contin. Dyn. Syst. 39, No. 5, 2893-2913 (2019). MSC: 35Q84 35A15 35G25 35K46 65L06 65J08 82C31 PDFBibTeX XMLCite \textit{S. Plazotta}, Discrete Contin. Dyn. Syst. 39, No. 5, 2893--2913 (2019; Zbl 1417.35202) Full Text: DOI arXiv
Shubina, M. V. Exact traveling wave solutions of one-dimensional parabolic-parabolic models of chemotaxis. (English) Zbl 1402.35064 Russ. J. Math. Phys. 25, No. 3, 383-395 (2018). MSC: 35C07 92C17 35K40 35K57 PDFBibTeX XMLCite \textit{M. V. Shubina}, Russ. J. Math. Phys. 25, No. 3, 383--395 (2018; Zbl 1402.35064) Full Text: DOI arXiv
Hashira, Takahiro Properties of blow-up solutions and their initial data for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. (English) Zbl 1401.35156 J. Math. Anal. Appl. 468, No. 2, 585-607 (2018). MSC: 35K51 35B44 35K59 35K65 35Q92 92C17 PDFBibTeX XMLCite \textit{T. Hashira}, J. Math. Anal. Appl. 468, No. 2, 585--607 (2018; Zbl 1401.35156) Full Text: DOI
Hashira, Takahiro; Ishida, Sachiko; Yokota, Tomomi Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. (English) Zbl 1394.35253 J. Differ. Equations 264, No. 10, 6459-6485 (2018). Reviewer: Christian Stinner (Darmstadt) MSC: 35K65 35B44 92C17 35Q92 PDFBibTeX XMLCite \textit{T. Hashira} et al., J. Differ. Equations 264, No. 10, 6459--6485 (2018; Zbl 1394.35253) Full Text: DOI
Zeng, Yong Existence of global bounded classical solution to a quasilinear attraction-repulsion chemotaxis system with logistic source. (English) Zbl 1469.35114 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 161, 182-197 (2017). MSC: 35K51 35A01 35A09 35B40 35K59 92C17 PDFBibTeX XMLCite \textit{Y. Zeng}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 161, 182--197 (2017; Zbl 1469.35114) Full Text: DOI
Laurençot, Philippe; Matioc, Bogdan-Vasile Self-similarity in a thin film Muskat problem. (English) Zbl 1386.35238 SIAM J. Math. Anal. 49, No. 4, 2790-2842 (2017). MSC: 35K65 35K40 35C06 35Q35 PDFBibTeX XMLCite \textit{P. Laurençot} and \textit{B.-V. Matioc}, SIAM J. Math. Anal. 49, No. 4, 2790--2842 (2017; Zbl 1386.35238) Full Text: DOI arXiv
Matthes, Daniel; Zinsl, Jonathan Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type. (English) Zbl 1371.35146 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 159, 316-338 (2017). MSC: 35K46 35D30 49J40 35K65 35A15 PDFBibTeX XMLCite \textit{D. Matthes} and \textit{J. Zinsl}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 159, 316--338 (2017; Zbl 1371.35146) Full Text: DOI arXiv
Gallouët, Thomas O.; Monsaingeon, Léonard A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows. (English) Zbl 1372.35126 SIAM J. Math. Anal. 49, No. 2, 1100-1130 (2017). MSC: 35K15 35K57 35K65 47J30 PDFBibTeX XMLCite \textit{T. O. Gallouët} and \textit{L. Monsaingeon}, SIAM J. Math. Anal. 49, No. 2, 1100--1130 (2017; Zbl 1372.35126) Full Text: DOI arXiv
Mimura, Yoshifumi Critical mass of degenerate Keller-Segel system with no-flux and Neumann boundary conditions. (English) Zbl 1364.35168 Discrete Contin. Dyn. Syst. 37, No. 3, 1603-1630 (2017). MSC: 35K65 35B33 47J30 35K40 PDFBibTeX XMLCite \textit{Y. Mimura}, Discrete Contin. Dyn. Syst. 37, No. 3, 1603--1630 (2017; Zbl 1364.35168) Full Text: DOI
Zinsl, Jonathan The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances. (English) Zbl 1360.35086 Discrete Contin. Dyn. Syst., Ser. S 10, No. 4, 919-933 (2017). MSC: 35K35 35A15 35D30 PDFBibTeX XMLCite \textit{J. Zinsl}, Discrete Contin. Dyn. Syst., Ser. S 10, No. 4, 919--933 (2017; Zbl 1360.35086) Full Text: DOI arXiv
Kinderlehrer, David; Monsaingeon, Léonard; Xu, Xiang A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations. (English) Zbl 1372.35167 ESAIM, Control Optim. Calc. Var. 23, No. 1, 137-164 (2017). MSC: 35K65 35K40 47J30 35Q92 35B33 PDFBibTeX XMLCite \textit{D. Kinderlehrer} et al., ESAIM, Control Optim. Calc. Var. 23, No. 1, 137--164 (2017; Zbl 1372.35167) Full Text: DOI arXiv
Laurençot, Philippe; Mizoguchi, Noriko Finite time blowup for the parabolic-parabolic Keller-Segel system with critical diffusion. (English) Zbl 1357.35060 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 1, 197-220 (2017). MSC: 35B44 35B33 35K65 35Q92 92C17 35K51 PDFBibTeX XMLCite \textit{P. Laurençot} and \textit{N. Mizoguchi}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 1, 197--220 (2017; Zbl 1357.35060) Full Text: DOI
Plazotta, Simon; Zinsl, Jonathan High-frequency limit of non-autonomous gradient flows of functionals with time-periodic forcing. (English) Zbl 1353.35011 J. Differ. Equations 261, No. 12, 6806-6855 (2016). MSC: 35A15 35G25 35K45 35D30 37B55 PDFBibTeX XMLCite \textit{S. Plazotta} and \textit{J. Zinsl}, J. Differ. Equations 261, No. 12, 6806--6855 (2016; Zbl 1353.35011) Full Text: DOI arXiv
Liu, Jian-Guo; Wang, Jinhuan A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model. (English) Zbl 1335.35103 Acta Appl. Math. 142, No. 1, 173-188 (2016). MSC: 35K55 35B45 35K65 92C17 35A01 35A02 PDFBibTeX XMLCite \textit{J.-G. Liu} and \textit{J. Wang}, Acta Appl. Math. 142, No. 1, 173--188 (2016; Zbl 1335.35103) Full Text: DOI
Zinsl, Jonathan Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusion. (English) Zbl 1338.35058 Discrete Contin. Dyn. Syst. 36, No. 5, 2915-2930 (2016). Reviewer: Philippe Laurençot (Toulouse) MSC: 35B40 35K45 35A15 35Q60 PDFBibTeX XMLCite \textit{J. Zinsl}, Discrete Contin. Dyn. Syst. 36, No. 5, 2915--2930 (2016; Zbl 1338.35058) Full Text: DOI arXiv
Kawakami, Tatsuki; Sugiyama, Yoshie Uniqueness theorem on weak solutions to the Keller-Segel system of degenerate and singular types. (English) Zbl 1336.35009 J. Differ. Equations 260, No. 5, 4683-4716 (2016). MSC: 35A02 92C17 35D30 35K65 PDFBibTeX XMLCite \textit{T. Kawakami} and \textit{Y. Sugiyama}, J. Differ. Equations 260, No. 5, 4683--4716 (2016; Zbl 1336.35009) Full Text: DOI
Zinsl, Jonathan A note on the variational analysis of the parabolic-parabolic Keller-Segel system in one spatial dimension. (Une note sur l’analyse variationelle du système de Keller-Segel parabolique-parabolique à une dimension spatiale.) (English. French summary) Zbl 1322.35055 C. R., Math., Acad. Sci. Paris 353, No. 9, 849-854 (2015). MSC: 35K45 92C17 35A01 35A15 35Q92 35D30 35B40 PDFBibTeX XMLCite \textit{J. Zinsl}, C. R., Math., Acad. Sci. Paris 353, No. 9, 849--854 (2015; Zbl 1322.35055) Full Text: DOI arXiv
Laurençot, Philippe; Matioc, Bogdan-Vasile A thin film approximation of the Muskat problem with gravity and capillary forces. (English) Zbl 1307.35137 J. Math. Soc. Japan 66, No. 4, 1043-1071 (2014). MSC: 35K45 35K65 35K58 47J30 35Q35 76A20 PDFBibTeX XMLCite \textit{P. Laurençot} and \textit{B.-V. Matioc}, J. Math. Soc. Japan 66, No. 4, 1043--1071 (2014; Zbl 1307.35137) Full Text: DOI arXiv Euclid
Zinsl, Jonathan Existence of solutions for a nonlinear system of parabolic equations with gradient flow structure. (English) Zbl 1302.35202 Monatsh. Math. 174, No. 4, 653-679 (2014). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K45 35K65 35A15 35Q92 92C17 35K59 PDFBibTeX XMLCite \textit{J. Zinsl}, Monatsh. Math. 174, No. 4, 653--679 (2014; Zbl 1302.35202) Full Text: DOI
Lippoth, Friedrich On the justification of the quasistationary approximation of several parabolic moving boundary problems. Part I. (English) Zbl 1296.35221 Nonlinear Anal., Real World Appl. 17, 1-22 (2014). MSC: 35R37 PDFBibTeX XMLCite \textit{F. Lippoth}, Nonlinear Anal., Real World Appl. 17, 1--22 (2014; Zbl 1296.35221) Full Text: DOI
Escher, Joachim; Matioc, Bogdan-Vasile Non-negative global weak solutions for a degenerated parabolic system approximating the two-phase Stokes problem. (English) Zbl 1288.35291 J. Differ. Equations 256, No. 8, 2659-2676 (2014). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K52 35K65 35Q35 35D30 76A20 PDFBibTeX XMLCite \textit{J. Escher} and \textit{B.-V. Matioc}, J. Differ. Equations 256, No. 8, 2659--2676 (2014; Zbl 1288.35291) Full Text: DOI arXiv
Carrillo, José Antonio; Lisini, Stefano; Mainini, Edoardo Uniqueness for Keller-Segel-type chemotaxis models. (English) Zbl 1277.35009 Discrete Contin. Dyn. Syst. 34, No. 4, 1319-1338 (2014). MSC: 35A02 35K45 35Q92 35K59 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Discrete Contin. Dyn. Syst. 34, No. 4, 1319--1338 (2014; Zbl 1277.35009) Full Text: DOI arXiv