Asymptotic behavior of solutions for linear parabolic equations with general measure data

Abstract

In this paper we deal with the asymptotic behavior as $t$ tends to infinity of solutions for linear parabolic equations whose model is $$\{\begin{array}{ll}{u}_t-\Delta u=\mu & \text{in}(0,T)\times \Omega ,\\ u(0,x)=u_0& \text{in}\Omega ,\end{array}$$ where $\mu$ is a general, possibly singular, Radon measure which does not depend on time, and $u_0\in L^1(\Omega )$. We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by G. Stampacchia) of the associated elliptic problem.

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• Renormalized solutions of nonlinear parabolic equations with general measure data