Local and nonlocal energy-based coupling models
Analysis of PDEs
2021-07-13 v1
Abstract
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way 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 deal with local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics.
Cite
@article{arxiv.2107.05083,
title = {Local and nonlocal energy-based coupling models},
author = {Gabriel Acosta and Francisco M. Bersetche and Julio D. Rossi},
journal= {arXiv preprint arXiv:2107.05083},
year = {2021}
}