An abstract approach to domain perturbation for parabolic equations and parabolic variational inequalities
Analysis of PDEs
2011-09-16 v1
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.
Keywords
Cite
@article{arxiv.1109.3257,
title = {An abstract approach to domain perturbation for parabolic equations and parabolic variational inequalities},
author = {Parinya Sa Ngiamsunthorn},
journal= {arXiv preprint arXiv:1109.3257},
year = {2011}
}