Nonlinear evolution equations are ubiquitous in applications and pose a variety of challenging mathematical questions, from well-posedness, to regularity. Variational methods provide far-reaching modeling and analytical tools. Among these, the Weighted Inertia-Energy-Dissipation () approach has already proved successful in a range of classical situations.

We aim at assessing the applicability of the WIDE variational principle out of its comfort zone, by targeting a number of hot and demanding research fronts. These include generalized doubly nonlinear flows, stochastic partial differential equations, conservations laws and fluids, and optimal control problems.

The WIDE variational approach consists in the minimization of a parameter-dependent, global-in-time functional and a passage to the limit in the parameter. We aim at proving that the minimizers of such parameter-dependent functional converge to solutions of the limiting nonlinear evolution problem.

This global variational approach paves the way to applying to nonlinear evolution problems the tools of the calculus of variations such as the Direct Method, $\Gamma$-convergence, and relaxation. The outcome will be novel existence and approximation theories. The program will be developed by a new international research team coordinated by Ulisse Stefanelli, with the cooperation of Goro Akagi (Sendai), Takeshi Fukao (Kyoto), and Hao Wu (Shanghai).

This project is financed by the Austrian Science Fund (FWF) with project number P 32788 and it is embedded within the activities of the Research Group in Applied Mathematics and Modeling at the University of Vienna.