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Spectral properties of stationary solutions of the nonlinear heat equation
Cazenave, Thierry (Université Pierre et Marie Curie (Paris))
Dickstein, Flavio (Universidade Federal do Rio de Janeiro. Instituto de Matemática)
Weissler, Fred B. (Université Paris 13)
Centre national de la recherche scientifique (França). Laboratoire Jacques-Louis Lions

Data: 2011
Resum: In this paper, we prove that if ψ is a radially symmetric, signchanging stationary solution of the nonlinear heat equation (NLH) u - ∆u = │u │ α u, in the unit ball of RN, N=3, with Dirichlet boundary conditions, then the solution of (NLH) with initial value λψ blows up infinite time if │λ - 1│ > 0 is sufficiently small and if α > 0 is sufficiently small. The proof depends on showing that the inner product of ψ with the first eigenfunction of the linearized operator L= - ∆ - (α + 1) │ψ│α is nonzero.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Semilinear heat equation ; Finite-time blowup ; Sign-changing stationary ; Solutions ; Linearized operator
Publicat a: Publicacions Matemàtiques, Vol. 55, Núm. 1 (2011) , p. 185-200, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_55111_09

16 p, 312.9 KB

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