Asymptotic analysis of solutions to parabolic systems
2009 (English)In: MATHEMATISCHE NACHRICHTEN, ISSN 0025-584X , Vol. 282, no 3, 430-458 p.Article in journal (Refereed) Published
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.
Asymptotic behaviour, parabolic system, Cauchy problem
IdentifiersURN: urn:nbn:se:liu:diva-18022DOI: 10.1002/mana.200710746OAI: oai:DiVA.org:liu-18022DiVA: diva2:214261