English

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.

Keywords

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

R2 v1 2026-06-28T13:52:40.220Z