On non-existence of global solutions to a class of stochastic heat equations

Mohammud Foondun; Rana D. Parshad

doi:10.1090/proc/12036

On non-existence of global solutions to a class of stochastic heat equations

Mohammud Foondun, Rana D. Parshad

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

We consider nonlinear parabolic SPDEs of the form ∂_tu = − (−Δ)^α/2u + b(u) + σ(u)ẇ, where ẇ denotes space-time white noise. The functions b and σ are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.

Original language	English
Pages (from-to)	4085-4094
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	9
DOIs	https://doi.org/10.1090/proc/12036
Publication status	Published - 6 Apr 2015
Externally published	Yes

Keywords

liapounov exponents
stable processes
stochastic partial differential equations
weak intermittence

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N2 - We consider nonlinear parabolic SPDEs of the form ∂tu = − (−Δ)α/2u + b(u) + σ(u)ẇ, where ẇ denotes space-time white noise. The functions b and σ are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.

AB - We consider nonlinear parabolic SPDEs of the form ∂tu = − (−Δ)α/2u + b(u) + σ(u)ẇ, where ẇ denotes space-time white noise. The functions b and σ are both locally Lipschitz continuous. Under some suitable conditions on the parameters of this SPDE, we show that the above equation has no random-field solution. This complements recent works of Khoshnevisan and his coauthors.

KW - liapounov exponents

KW - stable processes

KW - stochastic partial differential equations

KW - weak intermittence

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