Speaker
Description
We consider different measure-valued solvability concepts from the literature and show that they could be simplified by using the energy-variational structure of the underlying system of partial differential equations. In the considered examples, we prove that a measure-valued solution can be equivalently expressed as an energy-variational solution. The first concept represents the solution as a high-dimensional Young measure, whether for the second concept, only a scalar auxiliary variable is introduced and the formulation is relaxed to an energy-variational inequality. We investigate several examples stemming from interface dynamics, elasticity, and liquid crystals. The wide range of examples shows that this is a recurrent feature in evolution equations in general.
