NONLINEAR CROSS-DIFFUSION WITH SIZE EXCLUSION

被引：91

作者：

Burger, Martin ^{[1
]}

Di Francesco, Marco ^{[2
,4
]}

Pietschmann, Jan-Frederik ^{[3
]}

Schlake, Baebel ^{[1
]}

机构：

[1] Univ Munster, Inst Numer & Angew Math, D-48149 Munster, Germany

[2] Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67100 Laquila, Italy

[3] Univ Cambridge, DAMTP, Cambridge CB3 0WA, England

[4] WWU Univ Munster, Inst Computat & Appl Math, Munster, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 06期

关键词：

diffusion; size exclusion; cross-diffusion; ion channels; large-time behavior; KELLER-SEGEL MODEL; POPULATION-MODEL; EQUATIONS; PLANCK; CHEMOTAXIS; DENSITY; SYSTEM;

D O I：

10.1137/100783674

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions.

引用

页码：2842 / 2871

页数：30

共 48 条

[1]

Adams R., 1985, Sobolev Spaces

[2]

Ambrosio L., 2005, Lectures in Mathematics ETH Zurich

[3]

[Anonymous], 1968, TRANSLATIONS MATH MO

[4]

[Anonymous], 2003, CAN APPL MATH Q

[5] On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations [J].

Arnold, A ;

Markowich, P ;

Toscani, G ;

Unterreiter, A .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (1-2) :43-100

[6] Ion flow through narrow membrane channels: part II [J].

Barcilon, Victor ;

Chen, D.-P. ;

Eisenberg, R.S. .

SIAM Journal on Applied Mathematics, 1992, 52 (05) :1405-1425

[7]

Bregman L. M., 1967, USSR Comput Math Math Phys, V7, P200, DOI [10.1016/0041-5553(67)90040-7, DOI 10.1016/0041-5553(67)90040-7]

[8] Inverse total variation flow [J].

Burger, M. ;

Frick, K. ;

Osher, S. ;

Scherzer, O. .

MULTISCALE MODELING & SIMULATION, 2007, 6 (02) :366-395

[9]

BURGER M, 2010, NONLINEAR POIS UNPUB

[10]

Calvez V, 2008, COMMUN MATH SCI, V6, P417

← 1 2 3 4 5 →