Spectral properties of stationary solutions of the nonlinear heat equation

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│....

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Bibliographic Details
Authors: Cazenave, Thierry, Dickstein, Flavio, Weissler, Fred B.
Format: article
Publication Date:2011
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:65204
Online Access:https://ddd.uab.cat/record/65204
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55111_09
Access Level:Open access
Keyword:Semilinear heat equation
Finite-time blowup
Sign-changing stationary
Solutions
Linearized operator
Description
Summary: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│.