Abstract and Applied Analysis
Volume 2012 (2012), Article ID 312536, 17 pages
http://dx.doi.org/10.1155/2012/312536
Research Article

Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

Weisheng Niu1 and Hongtao Li2

1School of Mathematical Sciences, Anhui University, Hefei 230039, China
2School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 10 July 2012; Accepted 17 August 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 Weisheng Niu and Hongtao Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.