Asymptotic behavior of solutions for linear parabolic equations with general measure data
Francesco Petitta · Comptes Rendus Mathématique · 2007
In this Note we deal with the asymptotic behavior as t tends to infinity of solutions for linear parabolic equations whose model is { u t − Δ u = μ in ( 0 , T ) × Ω , u ( 0 , x ) = u 0 in Ω , where μ is a general, possibly singular, Radon measure which does not depend on time, and u 0 ∈ L 1 ( Ω ) . We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by Stampacchia (1965)) of the associated elliptic problem.