An existence and uniqueness result using bounded variation estimates in Galerkin approximations

Ramesh Mondal; Aditi Sengupta

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arXiv · 2312.09959

An existence and uniqueness result using bounded variation estimates in Galerkin approximations

Ramesh Mondal·Aditi Sengupta

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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.

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Ramesh Mondal, Aditi Sengupta. 2023-12-15. An existence and uniqueness result using bounded variation estimates in Galerkin approximations. https://arxiv.org/abs/2312.09959

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