A coupled anisotropic chemotaxis-fluid model: The case of two-sidedly degenerate diffusion

被引：13

作者：

Chamoun, Georges ^{[1
,2
,3
]}

Saad, Mazen ^{[1
]}

Talhouk, Raafat ^{[2
,3
]}

机构：

[1] Ecole Cent Nantes, UMR CNRS 6629, Lab Math Jean Leray, F-44321 Nantes, France

[2] Univ Libanaise, EDST, Hadath, Beyrouth, Lebanon

[3] Fac Sci I, Math Lab, Hadath, Beyrouth, Lebanon

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 09期

关键词：

Degenerate parabolic equation; Navier-Stokes equations; Heterogeneous and anisotropic diffusion; Global existence of solutions; GLOBAL EXISTENCE;

D O I：

10.1016/j.camwa.2014.04.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, the mathematical analysis of a model arising from biology consisting of diffusion, chemotaxis with volume filling effect and transport through an incompressible fluid, is studied. Motivated by numerical and modeling issues, the global-in-time existence of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of two-sidedly nonlinear degenerate diffusion and of anisotropic and heterogeneous diffusion tensors where we prove the global existence for a Chemotaxis-Navier-Stokes system in space dimensions less than or equal to four and we show the uniqueness of weak solutions for the Chemotaxis-Stokes system in two or three space dimensions under further assumptions. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：1052 / 1070

页数：19

共 23 条

[11] THE DEVELOPMENT OF CONCENTRATION GRADIENTS IN A SUSPENSION OF CHEMOTACTIC BACTERIA [J].

HILLESDON, AJ ;

PEDLEY, TJ ;

KESSLER, JO .

BULLETIN OF MATHEMATICAL BIOLOGY, 1995, 57 (02) :299-&

[12] INITIATION OF SLIME MOLD AGGREGATION VIEWED AS AN INSTABILITY [J].

KELLER, EF ;

SEGEL, LA .

JOURNAL OF THEORETICAL BIOLOGY, 1970, 26 (03) :399-&

[13]

Kinderlehrer C., 1980, PURE APPL MATH

[14]

Ladyzhenskaya O.A., 1969, REV ENGLARGE MATH IT, V2

[15]

Laurençot P, 2005, PROG NONLIN, V64, P273

[16]

Liu J.-G., 2011, ANN I H POINCARA ANA

[17]

Lorz A, 2012, COMMUN MATH SCI, V10, P555

[18] Mathematical analysis of radionuclides displacement in porous media with nonlinear adsorption [J].

Marpeau, Fabien ;

Saad, Mazen .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 228 (02) :412-439

[19]

OGUNTUASE J. A., 2001, J. Inequal. Pure Appl. Math., V2

[20]

Painter K., 2002, Can. Appl. Math. Q., V10, P501

← 1 2 3 →