Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:272

Article

Gabriel Iagar, Razvan^1,2  Sanchez, Ariel¹ 

[1] Univ Rey Juan Carlos, Dept Matemat Aplicada Ciencia & Ingn Mat & Tecnol, Madrid 28933, Spain

[2] Romanian Acad, Inst Math, POB 1-764, RO-014700 Bucharest, Romania

关键词: Reaction-diffusion equations;    Non-homogeneous reaction;    Blow up;    Self-similar solutions;    Phase space analysis;   

DOI  :  10.1016/j.jde.2020.10.006

来源: Elsevier

【 摘 要 】

We perform a thorough study of the blow up profiles associated to the following second order reaction-diffusion equation with non-homogeneous reaction: partial derivative(t)u = partial derivative(xx)(u(m)) + vertical bar x vertical bar(sigma) u(p), in the range of exponents 1 < p < m and sigma > 0. We classify blow up solutions in self-similar form, that are likely to represent typical blow up patterns for general solutions. We thus show that the non-homogeneous coefficient vertical bar x vertical bar(sigma) has a strong influence on the qualitative aspects related to the finite time blow up. More precisely, for sigma similar to 0, blow up profiles have similar behavior to the well-established profiles for the homogeneous case sigma = 0, and typically global blow up occurs, while for sigma > 0 sufficiently large, there exist blow up profiles for which blow up occurs only at space infinity, in strong contrast with the homogeneous case. This work is a part of a larger program of understanding the influence of unbounded weights on the blow up behavior for reaction-diffusion equations. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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