An existence result for a general non-linear parabolic equation with a spatial Dirichlet boundary condition through a variational approach, a new development

This short communication develops an existence result for a general non-linear parabolic equation. The method of proof comprises a variational approach for establishing a concerning solution existence at each instant of time, related to a model discretized in time. The main difference, concerning a previous version, refers to a rigourous development for proving the related minimizing sequences are uniformly bounded in norm, independently of a specific natural parameter N, which corresponds to the number of nodes for such a model discretized in time.