Partial Differential Equations
Asymptotic behavior of solutions for linear parabolic equations with general measure data
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 571-576.

In this Note we deal with the asymptotic behavior as t tends to infinity of solutions for linear parabolic equations whose model is

{utΔu=μin(0,T)×Ω,u(0,x)=u0inΩ,
where μ is a general, possibly singular, Radon measure which does not depend on time, and u0L1(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.

Dans cette Note nous traitons le comportement asymptotique, quand t tend vers l'infini, des solutions des équations paraboliques linéaires dont le modéle est :

{utΔu=μdans(0,T)×Ω,u(0,x)=u0dansΩ,
μ est une mesure de Radon générale, éventuellement singulière, qui ne dépend pas de t, et où u0L1(Ω). Nous montrons que la solution de dualité, qui existe et est unique, converge vers la solution de dualité (introduite par Stampacchia (1965)) du probléme elliptique associé.

Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.021
Petitta, Francesco 1

1 Dipartimento di Matematica, Università La Sapienza, Piazzale A. Moro, 2, 00185 Roma, Italy
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Petitta, Francesco. Asymptotic behavior of solutions for linear parabolic equations with general measure data. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 571-576. doi : 10.1016/j.crma.2007.03.021. http://www.numdam.org/articles/10.1016/j.crma.2007.03.021/

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