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Relaxed parabolic problems
Smolka, Maciej
2000
Abstract
Let $G_{n}$ be a sequence of open subsets of a given open and bounded
$\Omega\subset\mathbb{R}^{N}$. We study the asymptotic behaviour
of the solutions of parabolic equations $u_{n}'+Au_{n}=f_{n}\:\textrm{on}\: G_{n}$.
Assuming that the right-hand sides $f_{n}$ and the initial conditions
converge in a proper way we find the form of the limit problem without
any additional hypothesis on $G_{n}$. Our method is based on the
notion of elliptic $\gamma^{A}$-convergence.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Maciej Smolka, "Relaxed parabolic problems", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2000), pp. 147-171.
Languages
en
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