Blow-up properties for a degenerate parabolic system coupled via nonlinear boundary flux

Boundary value problems

Si Xu¹ 

[1] Department of Mathematics, Jiangxi Vocational College of Finance And Economics, Jiujiang, P.R. China

关键词: non-simultaneous blow-up;    blow-up rate;    nonlinear diffusion;    nonlinear boundary flux;    5B33;    35K65;    35K55;   

DOI  :  10.1186/s13661-015-0449-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the simultaneous and non-simultaneous blow-up problem for a system of two nonlinear diffusion equations in a bounded interval, coupled at the boundary in a nonlinear way. Under certain hypotheses on the initial data and parameters, we prove that non-simultaneous blow-up is possible. Moreover, we get some conditions on which simultaneous blow-up must occur, as well as the non-simultaneous blow-up conditions for every initial data. Furthermore, we get a result on the coexistence of both simultaneous and non-simultaneous blow-ups.

【 授权许可】

CC BY