Difusión no lineal en Madrid
Seminario conjunto de las universidades: UAM, UC3M, UCM, UPM y URJC

Nonlocal variational problems and 

applications to peridynamics

Resumen. We study nonlocal variational problems consisting of an energy of the form of a double integral involving the function but not its derivative. This general model includes the nonlocal singular p-Laplacian, but we also allow for nonconvex integrands. We focus on three aspects: existence of minimizers of the energy, limit passage from the nonlocal model to the local one, and relaxation (replacement of a problem without minimizers by a related problem with minimizers).

We will give applications to peridynamics, which is a model in Solid Mechanics, and in particular Elasticity, whose main assumption is that particles at a positive distance exert a force upon each other, whence the nonlocal nature of the model.

This talk is based on joint works with J. C. Bellido and P. Pedregal.

Organizado por los proyectos: MTM2014-52240-P y MTM2014-53037-P
Comité organizador: Matteo Bonforte, Mar González, Arturo de Pablo y Fernando Quirós