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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Lankeit, Johannes¹ 

[1] Univ Paderborn, Inst Math, Warburger Str 100, D-33098 Paderborn, Germany

关键词: Keller-Segel;    Chemotaxis;    Nonlinear diffusion;    Global existence;    Boundedness;   

DOI  :  10.1016/j.jde.2016.12.007

来源: Elsevier

【 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.

【 授权许可】

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