Minimizing movements and a two-scale method for nonconvex problems involving inertia

Abstract: When dealing with fully nonlinear, nonconvex, quasistatic (i.e. inertialess) problems in continuum mechanics, de Giorgi's method of minimizing movements has long been a staple for existence proofs. However by its very nature, it has always been restricted to purely dissipative, gradient flow-type systems. The aim of this talk is to present a new two-scale method, developed jointly with B. Benešová and S. Schwarzacher, which allows to add inertial, conservative effects by using the minimizing movements method as a stepping stone to solve an approximative time-delayed problem in the same nonlinear, nonconvex state space. Using a flow-map approach, this method is not only able to cope with problems in Lagrangian, but also with those in Eulerian and even mixed formulations. While the method itself is quite general, we will illustrate its application at several examples involving solids, fluids and their interaction.

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).