Energy-variational solutions for conservation laws

Robert Lasarzik (Wias, Berlino)

Abstract: Conservation laws form one of the most fundamental classes of partial differential equations modelling phenomena in continuum physics. Nevertheless, their mathematical analysis is cumbersome and not yet well understood away from the one-dimensional case and special examples. By introducing energy-variational solutions for a general class of conservation laws, a solvability concept is proposed that allows to prove existence and weak-strong uniqueness of solutions. These solutions are shown to coincide with established solvability concepts for the compressible Euler equations. Even though the solutions are not unique, several properties of the associated solution set are amenable for defining selection criteria via optimization in order to select the physical relevant solution.