Evolutionary variational inequalities as generalized solution concepts

Robert Lasarzik (WIAS)

Abstract.
Many phenomena in science and technology can be modeled by nonlinear PDEs. Since smooth solutions are not known to exist or are not reasonable for phenomena like shocks or turbulence, generalised solutions need to be considered. In this talk we consider different generalized formulations based on inequalities. For thermodynamically consistent phase-field models, entropic solutions based on a global energy and local entropy inequality are introduced. These have several advantages in comparison to a formulation based on the local energy balance. For liquid crystals dissipative solutions are introduced, which are based on a relative energy inequality. Finally, the novel concept of energy-variational solutions is introduced and compared to other solution concepts.