Nonlinear parabolic flows with dynamic flux on the boundary

TL;DR

This paper investigates nonlinear parabolic equations with dynamic boundary conditions, establishing existence and uniqueness of solutions through finite difference schemes and semigroup methods for time-dependent and invariant cases.

Contribution

It introduces a novel analysis of nonlinear divergence parabolic equations with Wentzell boundary conditions, providing rigorous solution existence and uniqueness results.

Findings

Existence and uniqueness of strong solutions are proven.

Solutions are constructed as limits of finite difference schemes.

Semigroup approach confirms results for time-invariant cases.

Abstract

A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and via a semigroup approach in the time-invariant case.