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

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.

25 pages. Comments and suggestions are welcome. Corrections to the proof of Theorem 1.2 are incorporated