Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

Weisheng Niu and Hongtao Li

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/312536

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:312536

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