Sign-changing stationary solutions and blowup for a nonlinear heat equation in dimension two

Consider the nonlinear heat equation v t - Δ v = | v | p - 1 v ( N L H ) in the unit ball of R 2 , with Dirichlet boundary condition. Let u p , K be a radially symmetric, sign-changing stationary solution having a fixed number K of nodal regions. We prove that the solution of (NLH) with initial valu...

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Bibliographic Details
Published in:Journal of evolution equations 2014-09, Vol.14 (3), p.617-633
Main Authors: Dickstein, Flávio, Pacella, Filomena, Sciunzi, Berardino
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Consider the nonlinear heat equation v t - Δ v = | v | p - 1 v ( N L H ) in the unit ball of R 2 , with Dirichlet boundary condition. Let u p , K be a radially symmetric, sign-changing stationary solution having a fixed number K of nodal regions. We prove that the solution of (NLH) with initial value λ u p , K blows up in finite time if | λ −1| > 0 is sufficiently small and if p is sufficiently large. The proof is based on the analysis of the asymptotic behavior of u p , K and of the linearized operator L = - Δ - p | u p , K | p - 1 .
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-014-0230-x