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

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In this paper we deal with the asymptotic behavior as t tends to infinity of solutions for linear parabolic equations whose model is cases uₜ-Δu = μ& in(0,T)×Ω,0.7 ex] u(0,x)=u₀ & inΩ, cases where μ is a general, possibly singular, Radon measure which does not depend on time, and u₀∈ L¹(Ω). 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.