Asymptotic analysis of solutions to parabolic systems
2008 (English)In: Journal of Global Optimization, ISSN 0925-5001, Vol. 40, no 01-Mar, 369-374 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. A consequence is that for kappa is an element of L-1(0,infinity), the solution behaves asymptotically as the solution to a parabolic system with time-independent coefficients.
Place, publisher, year, edition, pages
2008. Vol. 40, no 01-Mar, 369-374 p.
asymptotic behaviour, parabolic system, spectral splitting, perturbation
National CategoryEngineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-45914DOI: 10.1007/s10898-007-9200-yOAI: oai:DiVA.org:liu-45914DiVA: diva2:266810