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Asymptotic analysis of solutions to parabolic systems
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)In: MATHEMATISCHE NACHRICHTEN, ISSN 0025-584X , Vol. 282, no 3, 430-458 p.Article in journal (Refereed) Published
Abstract [en]

We study asymptotics as t -> infinity of solutions to a linear, parabolic system of equations with time-dependent coefficients in Omega x (0, infinity), where Omega is a bounded domain. On partial derivative Omega x (0, infinity) 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 kappa(t). This includes in particular situations when the coefficients may take different values on different parts of Omega and the boundaries between them can move with t but stabilize as t -> infinity. The main result is an asymptotic representation of solutions for large t. As a corollary, it is proved that if kappa epsilon L-1 (0, infinity), then the solution behaves asymptotically as the solution to a parabolic system with time-independent coefficients.

Place, publisher, year, edition, pages
2009. Vol. 282, no 3, 430-458 p.
Keyword [en]
Asymptotic behaviour, parabolic system, Cauchy problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-18022DOI: 10.1002/mana.200710746OAI: oai:DiVA.org:liu-18022DiVA: diva2:214261
Available from: 2009-05-04 Created: 2009-05-04 Last updated: 2009-05-04

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Kozlov, VladimirLanger, MikaelRand , Peter

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