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

Tej Eddine Ghoul

doi:10.1016/j.na.2011.05.089

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

Tej Eddine Ghoul

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	6105-6115
Number of pages	11
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	17
DOIs	https://doi.org/10.1016/j.na.2011.05.089
State	Published - 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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10.1016/j.na.2011.05.089

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title = "An extension of Dickstein's {"}small lambda{"} theorem for finite time blowup",

abstract = "In this paper we prove for 1L1( RN) with ∫RNφ=0 and ζ∈ C0(RN)∩W1,1(RN) with ∫RNζ≠0 such that φ=∂jζ that there exists {\=λ}>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<{\=λ}. This extends a similar result of Dickstein who treated the case ∫RNφ≠0 and 1",

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year = "2011",

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N2 - In this paper we prove for 1L1( 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

AB - In this paper we prove for 1L1( 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

KW - Blowup

KW - Local existence

KW - Nonlinear heat equation

KW - Rescaling

KW - Sign-changing solutions

KW - Weak initial data

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SP - 6105

EP - 6115

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 17

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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