An abstract approach to the Robin-Robin method

TL;DR

This paper extends an abstract framework for the Robin-Robin method to include initial-boundary value problems, broadening its applicability to linear and nonlinear elliptic and parabolic equations on Lipschitz domains.

Contribution

It demonstrates that the previously developed abstract approach can be applied to initial-boundary value problems, expanding the method's scope.

Findings

Framework now applicable to initial-boundary value problems

Unified treatment of elliptic and parabolic equations

Applicable to Lipschitz domains

Abstract

Recently, their has been development of an abstract approach to the Robin--Robin method, enabling the treatment of linear and nonlinear elliptic and parabolic equations on Lipschitz domains within one framework. However, previously this setting has not been applicable to initial-boundary value problems. The aim of this short note is therefore to demonstrate that this general framework can be applied to such problems as well.