Blow-up profiles and refined extensibility criteria in quasilinear Keller-Segel systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Freitag, Marcel¹ 

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

关键词: Classical solutions;    Blow-up;    Nonlinear parabolic equations;    Critical exponents;    Cell movement (chemotaxis etc.);   

DOI  :  10.1016/j.jmaa.2018.03.052

来源: Elsevier

【 摘 要 】

In this work we consider the system {u(t) = del center dot(D(u)del u) - del center dot(S(u)del v) in Omega x (0, infinity) v(t) = Delta v-v+u in Omega x (0, infinity), for a bounded domain Omega subset of R-n, n >= 2, where the functions D and S behave similarly to power functions. We prove the existence of classical solutions under Neumann boundary conditions and for smooth initial data. Moreover, we characterise the maximum existence time T-max of such a solution depending chiefly on the relation between the functions D and 5: We show that a finite maximum existence time also results in unboundedness in L-P-spaces for smaller p is an element of [1, infinity). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free