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

Tej-eddine Ghoul

    Research output: Contribution to journalArticle

    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 1 2011

    Fingerprint

    Finite Time Blow-up
    Blow-up
    Theorem

    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    An extension of Dickstein's "small lambda" theorem for finite time blowup. / Ghoul, Tej-eddine.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 74, No. 17, 01.12.2011, p. 6105-6115.

    Research output: Contribution to journalArticle

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