An existence and uniqueness result using bounded variation estimates in Galerkin approximations
Analysis of PDEs
2025-01-31 v5
Abstract
Bounded variation estimates of Galerkin approximations are established in order to extract an almost everywhere convergent subsequence of Galerkin approximations. As a result we prove existence of weak solutions of initial boundary value problems for quasilinear parabolic equations. Uniqueness of weak solutions is derieved applying a standard argument.
Cite
@article{arxiv.2312.09959,
title = {An existence and uniqueness result using bounded variation estimates in Galerkin approximations},
author = {Ramesh Mondal and Aditi Sengupta},
journal= {arXiv preprint arXiv:2312.09959},
year = {2025}
}
Comments
25 pages. Comments and suggestions are welcome. Corrections to the proof of Theorem 1.2 are incorporated