✦ LIBER ✦

Asymptotic analysis of solutions to parabolic systems

✍ Scribed by Vladimir Kozlov; Mikael Langer; Peter Rand

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 274 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200710746

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✦ Synopsis

Abstract

We study asymptotics as t → ∞ of solutions to a linear, parabolic system of equations with time‐dependent coefficients in Ω × (0, ∞), where Ω is a bounded domain. On ∂ Ω × (0, ∞) we prescribe the homogeneous Dirichlet boundary condition. For large values of t, the coefficients in the elliptic part are close to time‐independent coefficients in an integral sense which is described by a certain function κ (t). This includes in particular situations when the coefficients may take different values on different parts of Ω and the boundaries between them can move with t but stabilize as t → ∞. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if κ ∈ L^1^(0, ∞), then the solution behaves asymptotically as the solution to a parabolic system with time‐independent coefficients (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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