Weighted Energy-Dissipation approach to gradient flows

Abstract: The Weighted Energy-Dissipation variational approach has been extensively applied to gradient flows in the last decade. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter, such global minimizers converge, up to subsequences, to a solution of the gradient flow. After discussing such variational formulation in the context of classical gradient flows, we will focus on the semilinear gradient flows with state-dependent dissipation. This is partly based on a joint work with Goro Akagi and Ulisse Stefanelli.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)