Doumic, Marie; Hecht, Sophie; Perthame, Benoît; Peurichard, Diane Multispecies cross-diffusions: from a nonlocal mean-field to a porous medium system without self-diffusion. (English) Zbl 07812256 J. Differ. Equations 389, 228-256 (2024). MSC: 35Q92 92D25 35K55 35R09 35B25 35D30 76S05 PDFBibTeX XMLCite \textit{M. Doumic} et al., J. Differ. Equations 389, 228--256 (2024; Zbl 07812256) Full Text: DOI arXiv
Elbar, Charles; Perthame, Benoît; Poiatti, Andrea; Skrzeczkowski, Jakub Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states. arXiv:2305.06239 Preprint, arXiv:2305.06239 [math.AP] (2023). MSC: 35B40 35B45 35G20 35Q92 BibTeX Cite \textit{C. Elbar} et al., ``Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states'', Preprint, arXiv:2305.06239 [math.AP] (2023) Full Text: arXiv OA License
Torres, Nicolás; Perthame, Benoît; Salort, Delphine A multiple time renewal equation for neural assemblies with elapsed time model. (English) Zbl 1501.35398 Nonlinearity 35, No. 10, 5051-5075 (2022). MSC: 35Q82 35B40 35F20 35R09 92B20 92C20 PDFBibTeX XMLCite \textit{N. Torres} et al., Nonlinearity 35, No. 10, 5051--5075 (2022; Zbl 1501.35398) Full Text: DOI arXiv
Elbar, Charles; Perthame, Benoît; Skrzeczkowski, Jakub Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation. arXiv:2206.07451 Preprint, arXiv:2206.07451 [math.AP] (2022). MSC: 35B40 35B45 35G20 35Q92 BibTeX Cite \textit{C. Elbar} et al., ``Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation'', Preprint, arXiv:2206.07451 [math.AP] (2022) Full Text: arXiv OA License
Almeida, Luis; Bliman, Pierre-Alexandre; Nadin, Grégoire; Perthame, Benoît; Vauchelet, Nicolas Final size and convergence rate for an epidemic in heterogeneous populations. (English) Zbl 1473.92034 Math. Models Methods Appl. Sci. 31, No. 5, 1021-1051 (2021). MSC: 92D30 35Q92 35R09 45C05 45G15 PDFBibTeX XMLCite \textit{L. Almeida} et al., Math. Models Methods Appl. Sci. 31, No. 5, 1021--1051 (2021; Zbl 1473.92034) Full Text: DOI arXiv
Dębiec, Tomasz; Perthame, Benoît; Schmidtchen, Markus; Vauchelet, Nicolas Incompressible limit for a two-species model with coupling through Brinkman’s law in any dimension. (English. French summary) Zbl 1458.35421 J. Math. Pures Appl. (9) 145, 204-239 (2021). MSC: 35Q92 92C37 35B45 35K57 35K55 35K65 76A10 76N10 76S05 35R35 PDFBibTeX XMLCite \textit{T. Dębiec} et al., J. Math. Pures Appl. (9) 145, 204--239 (2021; Zbl 1458.35421) Full Text: DOI HAL
Fang, Di; Jin, Shi; Markowich, Peter; Perthame, Benoît Implicit and semi-implicit numerical schemes for the gradient flow of the formation of biological transport networks. (English) Zbl 1437.65095 SMAI J. Comput. Math. 5, 229-249 (2019). MSC: 65M06 92C35 76Z05 76S05 92E20 35J60 35K57 35R02 35Q92 PDFBibTeX XMLCite \textit{D. Fang} et al., SMAI J. Comput. Math. 5, 229--249 (2019; Zbl 1437.65095) Full Text: DOI
Gwiazda, Piotr; Perthame, Benoît; Świerczewska-Gwiazda, Agnieszka A two-species hyperbolic-parabolic model of tissue growth. (English) Zbl 1425.35198 Commun. Partial Differ. Equations 44, No. 12, 1605-1618 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35K65 35B45 76N10 35K55 35K57 92C37 PDFBibTeX XMLCite \textit{P. Gwiazda} et al., Commun. Partial Differ. Equations 44, No. 12, 1605--1618 (2019; Zbl 1425.35198) Full Text: DOI arXiv
Almeida, Luis; Bubba, Federica; Perthame, Benoît; Pouchol, Camille Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations. (English) Zbl 1423.35177 Netw. Heterog. Media 14, No. 1, 23-41 (2019). MSC: 35K55 35Q92 35Q84 65M08 65M22 92C17 PDFBibTeX XMLCite \textit{L. Almeida} et al., Netw. Heterog. Media 14, No. 1, 23--41 (2019; Zbl 1423.35177) Full Text: DOI arXiv
Mellet, Antoine; Perthame, Benoît; Quirós, Fernando A Hele-Shaw problem for tumor growth. (English) Zbl 1377.35245 J. Funct. Anal. 273, No. 10, 3061-3093 (2017). MSC: 35Q92 35K55 35B25 76D27 92C17 92C50 35Q35 76S05 PDFBibTeX XMLCite \textit{A. Mellet} et al., J. Funct. Anal. 273, No. 10, 3061--3093 (2017; Zbl 1377.35245) Full Text: DOI arXiv
Kim, Inwon C.; Perthame, Benoît; Souganidis, Panagiotis E. Free boundary problems for tumor growth: a viscosity solutions approach. (English) Zbl 1334.35360 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 138, 207-228 (2016). MSC: 35Q92 35K55 35B25 35D40 92C50 76D27 PDFBibTeX XMLCite \textit{I. C. Kim} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 138, 207--228 (2016; Zbl 1334.35360) Full Text: DOI arXiv
Carrillo, José Antonio; Perthame, Benoît; Salort, Delphine; Smets, Didier Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience. (English) Zbl 1336.35332 Nonlinearity 28, No. 9, 3365-3388 (2015). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35Q84 35K60 82C32 92B20 35B44 35B40 35Q92 PDFBibTeX XMLCite \textit{J. A. Carrillo} et al., Nonlinearity 28, No. 9, 3365--3388 (2015; Zbl 1336.35332) Full Text: DOI HAL
Haskovec, Jan; Markowich, Peter; Perthame, Benoit Mathematical analysis of a PDE system for biological network formation. (English) Zbl 1345.35120 Commun. Partial Differ. Equations 40, No. 5, 918-956 (2015). Reviewer: Mariano Rodríguez Ricard (La Habana) MSC: 35Q92 35B32 35K55 92C42 PDFBibTeX XMLCite \textit{J. Haskovec} et al., Commun. Partial Differ. Equations 40, No. 5, 918--956 (2015; Zbl 1345.35120) Full Text: DOI arXiv HAL
Perthame, Benoît; Seguin, Nicolas; Tournus, Magali A simple derivation of BV bounds for inhomogeneous relaxation systems. (English) Zbl 1316.35183 Commun. Math. Sci. 13, No. 2, 577-586 (2015). MSC: 35L60 35B40 35Q92 35L50 35B25 PDFBibTeX XMLCite \textit{B. Perthame} et al., Commun. Math. Sci. 13, No. 2, 577--586 (2015; Zbl 1316.35183) Full Text: DOI arXiv
Perthame, Benoît Some mathematical aspects of tumor growth and therapy. (English) Zbl 1373.35322 Jang, Sun Young (ed.) et al., Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13–21, 2014. Vol. I: Plenary lectures and ceremonies. Seoul: KM Kyung Moon Sa (ISBN 978-89-6105-804-9/hbk; 978-89-6105-803-2/set). 529-545 (2014). MSC: 35Q92 35K55 35B25 76D27 92C50 92D25 35Q35 PDFBibTeX XMLCite \textit{B. Perthame}, in: Proceedings of the International Congress of Mathematicians (ICM 2014), Seoul, Korea, August 13--21, 2014. Vol. I: Plenary lectures and ceremonies. Seoul: KM Kyung Moon Sa. 529--545 (2014; Zbl 1373.35322)
Tang, Min; Vauchelet, Nicolas; Cheddadi, Ibrahim; Vignon-Clementel, Irene; Drasdo, Dirk; Perthame, Benoît Composite waves for a cell population system modeling tumor growth and invasion. (English) Zbl 1321.35249 Ciarlet, Philippe G. (ed.) et al., Partial differential equations. Theory, control and approximation. In honor of the scientific heritage of Jacques-Louis Lions. Selected papers based on the presentations at the international conference on partial differential equations: theory, control and approximation, Shanghai, China, May 28 – June 1, 2012. Berlin: Springer (ISBN 978-3-642-41400-8/hbk; 978-3-642-41401-5/ebook). 401-429 (2014). MSC: 35Q92 35J60 35K57 74J30 92C10 92C37 65M06 35C07 76D27 PDFBibTeX XMLCite \textit{M. Tang} et al., in: Partial differential equations. Theory, control and approximation. In honor of the scientific heritage of Jacques-Louis Lions. Selected papers based on the presentations at the international conference on partial differential equations: theory, control and approximation, Shanghai, China, May 28 -- June 1, 2012. Berlin: Springer. 401--429 (2014; Zbl 1321.35249) Full Text: DOI
Tournus, Magali; Edwards, Aurélie; Seguin, Nicolas; Perthame, Benoît Analysis of a simplified model of the urine concentration mechanism. (English) Zbl 1262.35204 Netw. Heterog. Media 7, No. 4, 989-1018 (2012). MSC: 35Q92 65M08 35L60 92C35 34B45 PDFBibTeX XMLCite \textit{M. Tournus} et al., Netw. Heterog. Media 7, No. 4, 989--1018 (2012; Zbl 1262.35204) Full Text: DOI
Doumic, Marie; Marciniak-Czochra, Anna; Perthame, Benoît; Zubelli, Jorge P. A structured population model of cell differentiation. (English) Zbl 1235.35030 SIAM J. Appl. Math. 71, No. 6, 1918-1940 (2011). MSC: 35B35 35F10 35Q92 92C37 PDFBibTeX XMLCite \textit{M. Doumic} et al., SIAM J. Appl. Math. 71, No. 6, 1918--1940 (2011; Zbl 1235.35030) Full Text: DOI arXiv
Pakdaman, Khashayar; Perthame, Benoît; Salort, Delphine Dynamics of a structured neuron population. (English) Zbl 1267.35239 Nonlinearity 23, No. 1, 55-75 (2010). Reviewer: Eugen Mamontov (Gothenburg) MSC: 35Q92 35B35 92C20 PDFBibTeX XMLCite \textit{K. Pakdaman} et al., Nonlinearity 23, No. 1, 55--75 (2010; Zbl 1267.35239) Full Text: DOI
Mischler, Stéphane; Perthame, Benoît; Ryzhik, Lenya Stability in a nonlinear population maturation model. (English) Zbl 1020.92025 Math. Models Methods Appl. Sci. 12, No. 12, 1751-1772 (2002). Reviewer: Svitlana P.Rogovchenko (Famagusta) MSC: 92D25 35Q92 35F30 PDFBibTeX XMLCite \textit{S. Mischler} et al., Math. Models Methods Appl. Sci. 12, No. 12, 1751--1772 (2002; Zbl 1020.92025) Full Text: DOI
Gasser, I.; Markowich, P. A.; Perthame, B. Dispersion and moment lemmas revisited. (English) Zbl 0931.35135 J. Differ. Equations 156, No. 2, 254-281 (1999). Reviewer: Vadim Komkov (Florida) MSC: 35Q40 81U30 81Q15 PDFBibTeX XMLCite \textit{I. Gasser} et al., J. Differ. Equations 156, No. 2, 254--281 (1999; Zbl 0931.35135) Full Text: DOI Link