Some non-existence results for a class of stochastic partial differential equations

Mohammud Foondun, Wei Liu, Erkan Nane

Research output: Contribution to journalArticle

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Abstract

Consider the following stochastic partial differential equation,

tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andxRd.

The operator L is the generator of a strictly stable process and F˙ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.

Original languageEnglish
JournalJournal of Differential Equations
Publication statusAccepted/In press - 21 Dec 2017

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Forcing Term
Stable Process
Stochastic Partial Differential Equations
Random Field
Partial differential equations
Nonexistence
Initial conditions
Strictly
Operator
Class
Random field

Keywords

  • probability
  • partial differential equation

Cite this

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title = "Some non-existence results for a class of stochastic partial differential equations",
abstract = "Consider the following stochastic partial differential equation, ∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd. The operator L is the generator of a strictly stable process and F˙ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.",
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journal = "Journal of Differential Equations",
issn = "0022-0396",

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Some non-existence results for a class of stochastic partial differential equations. / Foondun, Mohammud; Liu, Wei; Nane, Erkan.

In: Journal of Differential Equations, 21.12.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Some non-existence results for a class of stochastic partial differential equations

AU - Foondun, Mohammud

AU - Liu, Wei

AU - Nane, Erkan

PY - 2017/12/21

Y1 - 2017/12/21

N2 - Consider the following stochastic partial differential equation, ∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd. The operator L is the generator of a strictly stable process and F˙ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.

AB - Consider the following stochastic partial differential equation, ∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd. The operator L is the generator of a strictly stable process and F˙ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.

KW - probability

KW - partial differential equation

UR - https://arxiv.org/abs/1611.07282v1

M3 - Article

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -