An abstract approach to domain perturbation for parabolic equations and parabolic variational inequalities

2011/09/15 by Parinya Sa Ngiamsunthorn, Ngiamsunthorn, Parinya Sa
Mathematics · #35B20 #35K90 #49J40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B20 #msc:35K90 #msc:49J40

paper · pdf · doi:10.48550/arxiv.1109.3257

arxiv created 2011/09/15 · arxiv updated 2011/09/16

Abstract

We study the behaviour of solutions of linear non-autonomous parabolic equations subject to Dirichlet or Neumann boundary conditions under perturbation of the domain. We prove that Mosco convergence of function spaces for non-autonomous parabolic problems is equivalent to Mosco convergence of function spaces for the corresponding elliptic problems. As a consequence, we obtain convergence of solutions of non-autonomous parabolic equations under domain perturbation by variational methods using the same characterisation of domains as in elliptic case. A similar technique can be applied to obtain convergence of weak solutions of parabolic variational inequalities when the underlying convex set is perturbed.

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