Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data. (16th September 2012)

• Record Type: Journal Article
• Authors: Niu, Weisheng; Li, Hongtao
• Other Names: Zelik Sergey V. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-09-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/312536
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let Ω be a smooth bounded domain in ℝ N, ( N ≥ 3 ) . We consider the asymptotic behavior of solutions to the following problem u t - d i v ( a ( x ) ∇ u ) + λ f ( u ) = μ in Ω × ℝ +, u = 0 on ∂ Ω × ℝ +, u ( x, 0 ) = u 0 ( x ) in Ω, where u 0 ∈ L 1 ( 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.