Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation
Analysis of PDEs
2017-12-14 v2
Abstract
In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and use form methods in a more general framework to accomplish our goal. A class of non-autonomous elliptic problems with dynamical boundary conditions on Lipschitz domains is also considered in this same context.
Keywords
Cite
@article{arxiv.1709.10123,
title = {Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation},
author = {Pedro T. P. Lopes and Marcone C. Pereira},
journal= {arXiv preprint arXiv:1709.10123},
year = {2017}
}
Comments
This is a new version of a previous paper submitted here in Arxiv. It has substantial changes from the previous one. A whole section was rewritten and some small mistakes were corrected