A one-dimensional Keller–Segel equation with a drift issued from the boundary
Tài liệu tham khảo
Aubin, 1963, Un théorème de compacité, C. R. Acad. Sci. Paris, 256, 5042
Biler, 1995, Existence and nonexistence of solutions for a model of gravitational interaction of particle III, Colloq. Math., 68, 229, 10.4064/cm-68-2-229-239
Biler, 1998, Global and exploding solutions for nonlocal quadratic evolution problems, SIAM J. Appl. Math., 59, 845, 10.1137/S0036139996313447
Blanchet, 2009, Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions, Calc. Var. Partial Differential Equations, 35, 133, 10.1007/s00526-008-0200-7
Blanchet, 2008, Infinite time aggregation for the critical Patlak–Keller–Segel model in R2, Comm. Pure Appl. Math., 61, 1449, 10.1002/cpa.20225
Blanchet, 2006, Two-dimensional Keller–Segel model: optimal critical mass and qualitative properties of the solutions, Electron. J. Differential Equations, 44
Calvez, 2006, Volume effects in the Keller–Segel model: energy estimates preventing blow-up, J. Math. Pures Appl., 86, 155, 10.1016/j.matpur.2006.04.002
V. Calvez, L. Corrias, A. Ebde, Blow-up, concentration phenomenon and global existence for the Keller–Segel model in high dimension, submitted for publication
V. Calvez, R.J. Hawkins, N. Meunier, R. Voituriez, Analysis of a self-organisation model for spontaneous cell polarization, in preparation
Calvez, 2007, Modified Keller–Segel system and critical mass for the log interaction kernel, vol. 429
Cieślak
Corrias, 2004, Global solutions of some chemotaxis and angiogenesis systems in high space dimensions, Milano J. of Math., 72, 1, 10.1007/s00032-003-0026-x
Dolbeault, 2004, Optimal critical mass in the two-dimensional Keller–Segel model in R2, C. R. Math. Acad. Sci. Paris, 339, 611, 10.1016/j.crma.2004.08.011
Dolbeault, 2009, The two-dimensional Keller–Segel model after blow-up, Discrete Contin. Dyn. Syst., 25, 109, 10.3934/dcds.2009.25.109
Hawkins, 2009, Rebuilding cytoskeleton roads: Active-transport-induced polarization of cells, Phys. Rev. E, 80, 040903, 10.1103/PhysRevE.80.040903
Herrero, 1996, Singularity formation in the one-dimensional supercooled Stefan problem, European J. Appl. Math., 7, 119, 10.1017/S0956792500002266
Herrero, 1996, Chemotactic collapse for the Keller–Segel model, J. Math. Biol., 35, 177, 10.1007/s002850050049
Horstmann, 2003, From 1970 until present: the Keller–Segel model in chemotaxis and its consequences. I, Jahresber. Deutsch. Math.-Verein., 105, 103
Horstmann, 2001, Blow-up in a chemotaxis model without symmetry assumptions, European J. Appl. Math., 12, 159, 10.1017/S0956792501004363
Jäger, 1992, On explosions of solutions to a system of partial differential equations modeling chemotaxis, Trans. Amer. Math. Soc., 329, 819, 10.2307/2153966
Keller, 1971, Model for chemotaxis, J. Theor. Biol., 30, 225, 10.1016/0022-5193(71)90050-6
Nagai, 1995, Blow-up of radially symmetric solutions to a chemotaxis system, Adv. Math. Sci., 5, 581
Perthame, 2007, Transport Equations in Biology, 10.1007/978-3-7643-7842-4
Velázquez, 2004, Point dynamics in a singular limit of the Keller–Segel model. I. Motion of the concentration regions, SIAM J. Appl. Math., 64, 1198, 10.1137/S0036139903433888
Velázquez, 2004, Point dynamics in a singular limit of the Keller–Segel model. II. Formation of the concentration regions, SIAM J. Appl. Math., 64, 1224, 10.1137/S003613990343389X