Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

We consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, where W˙H is the fractional noise, L˙ is a (pure jump) Lévy space-time white noise, Δ is Laplacian, and Δα=-(-Δ)α/2 is the fractional Laplacian generator on R, and f,σ:[0,T]×R×R→R are measurable functio...

Full description

Bibliographic Details
Main Authors: Dengfeng Xia, Litan Yan, Weiyin Fei
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2017/8059796
id doaj-43f7cef069054de29df2d5399d1c7603
record_format Article
spelling doaj-43f7cef069054de29df2d5399d1c76032020-11-24T20:41:30ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/80597968059796Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy ProcessDengfeng Xia0Litan Yan1Weiyin Fei2College of Information Science and Technology, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, ChinaCollege of Information Science and Technology, Donghua University, 2999 North Renmin Rd., Songjiang, Shanghai 201620, ChinaSchool of Mathematics and Physics, Anhui Polytechnic University, Wuhu, Anhui 241000, ChinaWe consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, where W˙H is the fractional noise, L˙ is a (pure jump) Lévy space-time white noise, Δ is Laplacian, and Δα=-(-Δ)α/2 is the fractional Laplacian generator on R, and f,σ:[0,T]×R×R→R are measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.http://dx.doi.org/10.1155/2017/8059796
collection DOAJ
language English
format Article
sources DOAJ
author Dengfeng Xia
Litan Yan
Weiyin Fei
spellingShingle Dengfeng Xia
Litan Yan
Weiyin Fei
Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
Mathematical Problems in Engineering
author_facet Dengfeng Xia
Litan Yan
Weiyin Fei
author_sort Dengfeng Xia
title Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
title_short Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
title_full Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
title_fullStr Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
title_full_unstemmed Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process
title_sort mixed fractional heat equation driven by fractional brownian sheet and lévy process
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2017-01-01
description We consider the stochastic heat equation of the form ∂u/∂t=(Δ+Δα)u+(∂f/∂x)(t,x,u)+σ(t,x,u)L˙+W˙H, where W˙H is the fractional noise, L˙ is a (pure jump) Lévy space-time white noise, Δ is Laplacian, and Δα=-(-Δ)α/2 is the fractional Laplacian generator on R, and f,σ:[0,T]×R×R→R are measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.
url http://dx.doi.org/10.1155/2017/8059796
work_keys_str_mv AT dengfengxia mixedfractionalheatequationdrivenbyfractionalbrowniansheetandlevyprocess
AT litanyan mixedfractionalheatequationdrivenbyfractionalbrowniansheetandlevyprocess
AT weiyinfei mixedfractionalheatequationdrivenbyfractionalbrowniansheetandlevyprocess
_version_ 1716824813457113088

Similar Items