Sign-changing stationary solutions and blowup for the two power nonlinear heat equation in a ball

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:454

Article

Ben Slimene, Byrame^1,2 

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Lab Equat Derivees Partielles,LRO3ES04, Tunis 2092, Tunisia

[2] Univ Paris 13, CNRS, Sorbonne Paris Cite, Lab Analyse Geometrie & Applicat,UMR 7539, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France

关键词: Semilinear heat equation;    Finite-time blow-up;    Sign-changing stationary solutions;    Linearized operator;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2017.05.009

来源: Elsevier

【 摘 要 】

Consider the nonlinear heat equation u(t) =Delta u + vertical bar u vertical bar(p-1) u - vertical bar u vertical bar(q-1)u, where t >= 0 and x is an element of Omega, the unit ball of R-N, N >= 3, with Dirichlet boundary conditions. Let h be a radially symmetric, sign-changing stationary solution of (0.1). We prove that the solution of (0.1) with initial value lambda h blows up in finite time if vertical bar lambda-1 vertical bar>0 is sufficiently small and if 1 < q < ps = N+2/N-2 and p sufficiently close to ps. This proves that the set of initial data for which the solution is global is not star -shaped around 0. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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