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In this paper we deal with the asymptotic behavior as $t$ tends to infinityof solutions for linear parabolic equations whose model is $$ \begin{cases}u_{t}-\Delta u = \mu & \text{in}\ (0,T)\times\Omega,\\[0.7 ex] u(0,x)=u_0 &\text{in}\ \Omega, \end{cases} $$ where $\mu$ is a general, possibly singular,Radon measure which does not depend on time, and $u_0\in L^{1}(\Omega)$. Weprove that the duality solution, which exists and is unique, converges to theduality solution (as introduced by G. Stampacchia) of the associated ellipticproblem.

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