Local existence of solutions and comparison principle for initial boundary value problem with nonlocal boundary condition for a nonlinear parabolic equation with memory
Analysis of PDEs
2023-06-21 v2
Abstract
We consider an initial value problem for a nonlinear parabolic equation with memory under nonlinear nonlocal boundary condition. In this paper we study classical solutions. We establish the existence of a local maximal solution. It is shown that under some conditions a supersolution is not less than a subsolution. We find conditions for the positiveness of solutions. As a consequence of the positiveness of solutions and the comparison principle of solutions, we prove the uniqueness theorem.
Keywords
Cite
@article{arxiv.2305.18767,
title = {Local existence of solutions and comparison principle for initial boundary value problem with nonlocal boundary condition for a nonlinear parabolic equation with memory},
author = {Alexander Gladkov},
journal= {arXiv preprint arXiv:2305.18767},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1602.05018