Heat equation with dynamical boundary conditions of reactive-diffusive type

TL;DR

This paper studies a heat equation with a reactive-diffusive dynamical boundary condition involving the Laplace-Beltrami operator, establishing well-posedness and regularity of solutions in a bounded domain.

Contribution

It introduces and analyzes a novel boundary condition of reactive-diffusive type for the heat equation, proving well-posedness and regularity results.

Findings

Proved well-posedness of the heat equation with reactive-diffusive boundary conditions.

Established regularity properties of solutions.

Extended the understanding of boundary conditions involving the Laplace-Beltrami operator.

Abstract

This paper deals with the heat equation posed in a bounded regular domain coupled with a dynamical boundary condition of reactive-diffusive type, involving the Laplace-Beltrami operator. We prove well-posedness of the problem together with regularity of the solutions.