Nonlinear evolution problems present a variety of challenging mathematical questions ranging from well-posedness, to qualitative behavior of solutions, to approximation. Variational methods bear a paramount importance in this context by providing novel formulations and efficient tools for modeling, analysis, and simulations.

This project focuses on a global variational approach, the Weighted Inertia-Dissipation-Energy (WIDE) principle, for nonlinear evolution. The WIDE principle allows to reformulate a remarkable variety of evolution systems of applicative relevance in terms of a minimization plus a limit passage. This reformulation paves the way for tackling evolution problems with techniques of the Calculus of Variations such as the Direct Method, Gamma-convergence, and relaxation.

We aim at extending the available theory for the WIDE variational approach and apply it to nonconvex evolution problems, f ocusing both on well-posedness and on approximability results. Moreover, we will exploit the WIDE principle for modeling and solving existence issues in dynamic problems in materials.

This project is embedded within the activities of the Research Group in Applied Mathematics and Modeling at the University of Vienna.