The role of non-linear diffusion in non-simultaneous blow-up

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:308

Article

Brändle, C ; Quirós, F ; Rossi, JD

关键词: blow-up;    parabolic system;    non-linear diffusion;   

DOI  :  10.1016/j.jmaa.2004.11.004

来源: Elsevier

【 摘 要 】

We study a parabolic system of two non-linear reaction-diffusion equations completely coupled through source terms and with power-like diffusivity. Under adequate hypotheses on the initial data, we prove that non-simultaneous blow-up is sometimes possible; i.e., one of the components blows up while the other remains bounded. The conditions for non-simultaneous blow-up rely strongly on the diffusivity parameters and significant differences appear between the fast-diffusion and the porous medium case. Surprisingly, flat (homogeneous in space) solutions are not always a good guide to determine whether non-simultaneous blow-up is possible. (c) 2004 Elsevier Inc. All rights reserved.

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