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Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

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  • Weisheng Niu
  • Hongtao Li

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.

Suggested Citation

  • Weisheng Niu & Hongtao Li, 2012. "Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:312536
    DOI: 10.1155/2012/312536
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    References listed on IDEAS

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    1. Lifang Niu & Jianwen Zhang, 2012. "Existence of Global Attractors for the Nonlinear Plate Equation with Memory Term," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-7, October.
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