Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

TL;DR

This paper investigates linear nonautonomous parabolic systems with dynamic boundary conditions and establishes local existence and uniqueness of classical solutions for related quasilinear systems with nonlinear boundary conditions.

Contribution

It provides new theoretical results on the existence and uniqueness of solutions for complex parabolic systems with dynamic and nonlinear boundary conditions.

Findings

Proved local existence of classical solutions.

Established uniqueness of solutions.

Extended results to nonlinear dynamic boundary conditions.

Abstract

We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear dynamic boundary conditions.