An extension of Dickstein's "small lambda" theorem for finite time blowup

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Abstract

In this paper we prove for 1<p<1+1N+1, φ∈L1( RN) with ∫RNφ=0 and ζ∈ C0(RN)∩W1,1(RN) with ∫RNζ≠0 such that φ=∂jζ that there exists λ̄>0 such that the solution u of the equation ut-Δu=|u|p-1u with u(0)=λφ blows up in finite time for all 0<λ<λ̄. This extends a similar result of Dickstein who treated the case ∫RNφ≠0 and 1<p<1+2N.

Original languageEnglish (US)
Pages (from-to)6105-6115
Number of pages11
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number17
DOIs
StatePublished - Dec 2011

Keywords

  • Blowup
  • Local existence
  • Nonlinear heat equation
  • Rescaling
  • Sign-changing solutions
  • Weak initial data

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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