Dynamic bilateral boundary conditions on interfaces

TL;DR

This paper investigates elliptic boundary value problems with discontinuous coefficients in a bidomain, introducing generalized dynamic boundary conditions like Wentzell and Signorini types, and develops solutions through time discretization.

Contribution

It extends the analysis of elliptic problems by incorporating complex dynamic boundary conditions and nonlinearities within a bidomain setting.

Findings

Established existence of generalized solutions

Analyzed effects of non-constant coefficients

Developed a time discretization method for solutions

Abstract

Two boundary value problems for an elliptic equation in divergence form with bounded discontinuous coefficient are studied in a bidomain. On the interface, generalized dynamic boundary conditions such as of the Wentzell-type and Signorini-type transmission are considered in a subdifferential form. Several non-constant coefficients and nonlinearities are the main objective of the present work. Generalized solutions are built via time discretization.