Marc Rieger, Department of Mathematical Sciences, Carnegie Mellon University.
" Nonconvex Dynamical Problems "
We study partial differential equations of parabolic and hyperbolic type with nonconvex energy density. In particular existence theorems for Young measure solutions to nonconvex elastodynamical equations as can be used to desribe the evolution of microstructures in crystals are given. Moreover we present approximation schemes and numerical calculations of these solutions. The last part of the talk gives some (surprising) results on the regularity of H\"older solutions to vector-valued parabolic equations.
October 9, 2001