Boundary variation for non-autonomous parabolic equations with Neumann boundary condition

摘要

We study the behavior of solutions of non-autonomous parabolic equations subject to Neumann boundary condition under perturbation of the domain. We prove the convergence of solutions of parabolic equations under domain perturbation by variational methods using suitable assumptions on the sequence of perturbed domains which also give the convergence of solutions under domain perturbation for elliptic equations.