Blowup solutions for a reaction-diffusion system with exponential nonlinearities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Ghoul, Tej-Eddine¹  Van Tien Nguyen¹  Zaag, Hatem² 

[1] New York Univ Abu Dhabi, POB 129188, Abu Dhabi, U Arab Emirates

[2] Univ Paris 13, Sorbonne Paris Cite, LAGA, CNRS UMR 7539, F-93430 Villetaneuse, France

关键词: Blowup solution;    Blowup profile;    Stability;    Semilinear parabolic system;   

DOI  :  10.1016/j.jde.2018.02.022

来源: Elsevier

【 摘 要 】

We consider the following parabolic system whose nonlinearity has no gradient structure: {partial derivative(t)u = Lambda u + e(pv), partial derivative(t)v = mu Lambda v + e(qu), u(., 0) = u(0), v(., 0) = v(0), p, q, mu > 0, in the whole space R-N. We show the existence of a stable blowup solution and obtain a complete description of its singularity formation. The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. In particular, our analysis uses neither the maximum principle nor the classical methods based on energy-type estimates which are not supported in this system. The stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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