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

Mohammud Foondun; Wei Liu; Erkan Nane

doi:10.1016/j.jde.2018.08.039

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

Mohammud Foondun, Wei Liu, Erkan Nane

Mathematics And Statistics

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Abstract

Considerthe following stochastic partial differential equation,

∂tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andx∈Rd.

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

Original language	English
Pages (from-to)	2575-2596
Number of pages	22
Journal	Journal of Differential Equations
Volume	266
Issue number	5
Early online date	23 Aug 2018
DOIs	https://doi.org/10.1016/j.jde.2018.08.039
Publication status	Published - 15 Feb 2019

Keywords

probability
partial differential equation
space–time white noise
space colored noise
fractional stochastic equation

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10.1016/j.jde.2018.08.039

Foondun-etal-AAP-2018-Some-non-existence-results-for-a-class-of-stochastic (1)Accepted author manuscript, 232 KB

Cite this

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title = "Some non-existence results for a class of stochastic partial differential equations",

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

keywords = "probability, partial differential equation, space–time white noise, space colored noise, fractional stochastic equation",

author = "Mohammud Foondun and Wei Liu and Erkan Nane",

year = "2019",

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doi = "10.1016/j.jde.2018.08.039",

language = "English",

volume = "266",

pages = "2575--2596",

journal = "Journal of Differential Equations",

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

AU - Foondun, Mohammud

AU - Liu, Wei

AU - Nane, Erkan

PY - 2019/2/15

Y1 - 2019/2/15

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

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

KW - probability

KW - partial differential equation

KW - space–time white noise

KW - space colored noise

KW - fractional stochastic equation

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

U2 - 10.1016/j.jde.2018.08.039

DO - 10.1016/j.jde.2018.08.039

M3 - Article

SN - 0022-0396

VL - 266

SP - 2575

EP - 2596

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

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

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Mohammud Foondun

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

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Mohammud Foondun

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