Peridynamics is a nonlocal elasticity theory based on differences in the deformation instead of the deformation gradient. It is therefore believed to be suitable to describe long range forces as well as material failure. In this talk, we will give an introduction into the theory of peridynamics and consider its equation of motion as a nonlinear second order evolution equation. We present results on existence of weak and measure-valued solutions in the absence of any monotonicity assumption on the peridynamic operator. The method of proof also applies to other nonlocal partial differential equations. This is joint work with Etienne Emmrich.

Dimitri Puhst received both his Bachelor‘s and Master’s degree in Techno mathematics at TU Berlin 2010 and 2012, respectively. He then joined the differential equations research group of Professor Emmrich at TU Berlin to focus on his PhD studies.  Currently, he is working on nonlinear nonlocal evolution equations with applications in elasticity theory.