Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

Let Ω be a smooth bounded domain in ℝN,(N≥3). We consider the asymptotic behavior of solutions to the following problem ut-div(a(x)∇u)+λf(u)=μ  in  Ω×ℝ+,u=0  on  ∂Ω×ℝ+,  u(x,0)=u0(x)  in  Ω, where u0∈L1(Ω), μ is a finite Radon measure independent of time. We provide the existence and uniqueness resu...

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Main Authors: Weisheng Niu, Hongtao Li
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/312536
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spelling doaj-fb1beda79d764979b5b23edbca9eef892020-11-24T22:00:33ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/312536312536Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular DataWeisheng Niu0Hongtao Li1School of Mathematical Sciences, Anhui University, Hefei 230039, ChinaSchool of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, ChinaLet Ω be a smooth bounded domain in ℝN,(N≥3). We consider the asymptotic behavior of solutions to the following problem ut-div(a(x)∇u)+λf(u)=μ  in  Ω×ℝ+,u=0  on  ∂Ω×ℝ+,  u(x,0)=u0(x)  in  Ω, where u0∈L1(Ω), μ is a finite Radon measure independent of time. We provide the existence and uniqueness results on the approximated solutions. Then we establish some regularity results on the solutions and consider the long-time behavior.http://dx.doi.org/10.1155/2012/312536
collection DOAJ
language English
format Article
sources DOAJ
author Weisheng Niu
Hongtao Li
spellingShingle Weisheng Niu
Hongtao Li
Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
Abstract and Applied Analysis
author_facet Weisheng Niu
Hongtao Li
author_sort Weisheng Niu
title Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
title_short Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
title_full Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
title_fullStr Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
title_full_unstemmed Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
title_sort asymptotic behavior of approximated solutions to parabolic equations with irregular data
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description Let Ω be a smooth bounded domain in ℝN,(N≥3). We consider the asymptotic behavior of solutions to the following problem ut-div(a(x)∇u)+λf(u)=μ  in  Ω×ℝ+,u=0  on  ∂Ω×ℝ+,  u(x,0)=u0(x)  in  Ω, where u0∈L1(Ω), μ is a finite Radon measure independent of time. We provide the existence and uniqueness results on the approximated solutions. Then we establish some regularity results on the solutions and consider the long-time behavior.
url http://dx.doi.org/10.1155/2012/312536
work_keys_str_mv AT weishengniu asymptoticbehaviorofapproximatedsolutionstoparabolicequationswithirregulardata
AT hongtaoli asymptoticbehaviorofapproximatedsolutionstoparabolicequationswithirregulardata
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