Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion

被引：99
|
作者：
Lankeit, Johannes [1 ]
机构：
[1] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 262卷 / 07期
关键词：
Keller-Segel; Chemotaxis; Nonlinear diffusion; Global existence; Boundedness; KELLER-SEGEL SYSTEM; TRAVELING-WAVES; WELL-POSEDNESS; USERS GUIDE; EQUATIONS; STABILITY; BACTERIA;
D O I：
10.1016/j.jde.2016.12.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show the existence of locally bounded global solutions to the chemotaxis system {u(t) = del.((u)del u) - del.(u/v del v) in Omega x(0, infinity) v(t) = Delta v - uv in Omega x(0, infinity) partial derivative v(u) = partial derivative(v)v = 0 in Omega x(0, infinity) u(., 0) = u(0,) v(., 0) = v(0) in Omega in smooth bounded domains Omega subset of R-N, N >= 2, for D(u) >= delta Um-1 with some delta > 0, provided that m > 1+ N/4. (C) 2016 Elsevier Inc. All rights reserved.
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页码：4052 / 4084
页数：33
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