### Abstract

In this paper we prove for 1<p<1+1N+1, φ∈^{L1}( ^{RN}) with ∫_{RN}φ=0 and ζ∈ ^{C0}(^{RN})∩W1^{,1}(^{RN}) with ∫_{RN}ζ≠0 such that φ=^{∂j}ζ that there exists λ̄>0 such that the solution u of the equation ^{ut}-Δu=|^{u|p-1}u 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 ∫_{RN}φ≠0 and 1<p<1+2N.

Original language | English (US) |
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Pages (from-to) | 6105-6115 |

Number of pages | 11 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 74 |

Issue number | 17 |

DOIs | |

State | Published - Dec 1 2011 |

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### 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.

Research output: Contribution to journal › Article

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 74, no. 17, pp. 6105-6115. https://doi.org/10.1016/j.na.2011.05.089

}

TY - JOUR

T1 - An extension of Dickstein's "small lambda" theorem for finite time blowup

AU - Ghoul, Tej-eddine

PY - 2011/12/1

Y1 - 2011/12/1

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

UR - http://www.scopus.com/inward/record.url?scp=80051597718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051597718&partnerID=8YFLogxK

U2 - 10.1016/j.na.2011.05.089

DO - 10.1016/j.na.2011.05.089

M3 - Article

VL - 74

SP - 6105

EP - 6115

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 17

ER -