I am a PhD student at TU Berlin funded by a stipend of the Berlin Mathematical School (BMS). I am working on the subject of stochastic perturbations of second order in time PDEs in collaboration with Prof. Etienne Emmrich.
Up until january I have written my master thesis with Prof. Emmrich. There I treated the mathematical analysis of peridynamic theory which in turn is centered around a second order in time PDE related to continuum mechanics.
Building upon the work of Prof. Emmrich and Dimitri Puhst, a main part of my work was a consistent mathematical formulation of the state-based peridynamik theory introduced in the paper Silling et al, 2007: Peridynamic states and constitutive modeling. Further I try to give a framework for classical and weak solutions for the resulting nonlocal differential equations. The letter is based on the methods developped in the Paper Emmrich & Puhst, 2015: Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics.
A first peak at my work you can see in the slides of my two talk in the working group seminar: About states and ideas for classical solutions to the equation as well as a primer on the weak theory.