Some properties of non-linear fractional stochastic heat equations on bounded domains

Mohammud Foondun; Ngartelbaye Guerngar; Erkan Nane

Some properties of non-linear fractional stochastic heat equations on bounded domains

Mohammud Foondun, Ngartelbaye Guerngar, Erkan Nane

Mathematics And Statistics

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Abstract

Consider the following stochastic partial differential equation,∂tut(x) = Lut(x) + ξσ(ut(x)) ˙F (t, x),where ξ is a positive parameter and σ is a globally Lipschitz continuous function. The stochastic forcing term ˙F (t, x) is white in time but possibly colored in space. The operator L is a non-local operator. We study the behaviour of the solution with respect to the parameter ξ, extending the results in [8] and [11].

Original language	English
Journal	Chaos, Solitons and Fractals
Publication status	Accepted/In press - 28 Mar 2017

Keywords

stochastic fractional PDEs
large time behavior
colored noise

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Foodun-etal-CSF-2017-Some-properties-of-non-linear-fractional-stochastic-heat-equations-on-boundedAccepted author manuscript, 157 KBLicence: CC BY-NC-ND 4.0

http://www.sciencedirect.com/science/journal/09600779/99

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title = "Some properties of non-linear fractional stochastic heat equations on bounded domains",

abstract = "Consider the following stochastic partial differential equation,∂tut(x) = Lut(x) + ξσ(ut(x)) ˙F (t, x),where ξ is a positive parameter and σ is a globally Lipschitz continuous function. The stochastic forcing term ˙F (t, x) is white in time but possibly colored in space. The operator L is a non-local operator. We study the behaviour of the solution with respect to the parameter ξ, extending the results in [8] and [11].",

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T1 - Some properties of non-linear fractional stochastic heat equations on bounded domains

AU - Foondun, Mohammud

AU - Guerngar, Ngartelbaye

AU - Nane, Erkan

PY - 2017/3/28

Y1 - 2017/3/28

N2 - Consider the following stochastic partial differential equation,∂tut(x) = Lut(x) + ξσ(ut(x)) ˙F (t, x),where ξ is a positive parameter and σ is a globally Lipschitz continuous function. The stochastic forcing term ˙F (t, x) is white in time but possibly colored in space. The operator L is a non-local operator. We study the behaviour of the solution with respect to the parameter ξ, extending the results in [8] and [11].

AB - Consider the following stochastic partial differential equation,∂tut(x) = Lut(x) + ξσ(ut(x)) ˙F (t, x),where ξ is a positive parameter and σ is a globally Lipschitz continuous function. The stochastic forcing term ˙F (t, x) is white in time but possibly colored in space. The operator L is a non-local operator. We study the behaviour of the solution with respect to the parameter ξ, extending the results in [8] and [11].

KW - stochastic fractional PDEs

KW - large time behavior

KW - colored noise

UR - http://www.sciencedirect.com/science/journal/09600779/99

M3 - Article

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -