ON NON-EXISTENCE OF GLOBAL SOLUTIONS TO A CLASS OF STOCHASTIC HEAT EQUATIONS

Mohammud Foondun; Rana Parshad

doi:10.1090/proc/12036

ON NON-EXISTENCE OF GLOBAL SOLUTIONS TO A CLASS OF STOCHASTIC HEAT EQUATIONS

Mohammud Foondun, Rana Parshad

Computer, Electrical and Mathematical Sciences and Engineering

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

7 Scopus citations

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 (US)
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
State	Published - 2015

Bibliographical note

KAUST Repository Item: Exported on 2021-07-06
Acknowledgements: The authors thank a very careful referee whose comments lead to a more accurate version of this paper

ASJC Scopus subject areas

Applied Mathematics
General Mathematics

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https://repository.kaust.edu.sa/bitstream/10754/669941/1/Articlefile1.pdf

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title = "ON NON-EXISTENCE OF GLOBAL SOLUTIONS TO A CLASS OF STOCHASTIC HEAT EQUATIONS",

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.",

author = "Mohammud Foondun and Rana Parshad",

note = "KAUST Repository Item: Exported on 2021-07-06 Acknowledgements: The authors thank a very careful referee whose comments lead to a more accurate version of this paper",

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AU - Foondun, Mohammud

AU - Parshad, Rana

N1 - KAUST Repository Item: Exported on 2021-07-06 Acknowledgements: The authors thank a very careful referee whose comments lead to a more accurate version of this paper

PY - 2015

Y1 - 2015

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.

UR - http://hdl.handle.net/10754/669941

UR - http://www.ams.org/proc/2015-143-09/S0002-9939-2015-12036-9/

UR - http://www.scopus.com/inward/record.url?scp=84932614482&partnerID=8YFLogxK

U2 - 10.1090/proc/12036

DO - 10.1090/proc/12036

M3 - Article

SN - 1088-6826

VL - 143

SP - 4085

EP - 4094

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 9

ER -

ON NON-EXISTENCE OF GLOBAL SOLUTIONS TO A CLASS OF STOCHASTIC HEAT EQUATIONS

Abstract

Bibliographical note

ASJC Scopus subject areas

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