Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data
Weisheng Niu, Hongtao Li · Abstract and Applied Analysis · 2012
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.