Asymptotic Behavior of Approximated Solutions to Parabolic Equations with Irregular Data

Abstract EN

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.