Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem | Zendy

Juan-Luis V aacute zquez | Zendy; Philippe Souplet | Zendy

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Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem

Author(s) -

Juan-Luis V aacute zquez,

Philippe Souplet

Publication year - 2005

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2006.14.221

Subject(s) - singularity , convection , boundary (topology) , steady state (chemistry) , diffusion , mathematics , mathematical analysis , feature (linguistics) , physics , mechanics , thermodynamics , chemistry , philosophy , linguistics

This paper is devoted to analyze a case of singularity formation in infinite time for a semilinear heat equation involving linear diffusion and superlinear convection. A feature to be noted is that blow-up happens not for the main unknown but for its derivative. The singularity builds up at the boundary. The formation of inner and outer regions is examined, as well as the matching between them. As a consequence, we obtain the precise exponential rates of blow-up in infinite time.

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