Local and nonlocal energy-based coupling models

Abstract

In this paper we study two different ways of coupling a local operator with a nonlocal one so that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation, and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this paper we extend these ideas to local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics.