Degenerate Parabolic Differential Equations of Fourth Order and a Plasticity Model with Non-Local Hardening

Abstract

By the means of energy estimates we prove existence and non-negativity results for degenerate parabolic partial differential equations of fourth order in arbitrary space dimensions. In addition, we present an elasto-viscoplastic model of Norton-Hoff type with isotropic, non-local hardening which takes the formation of dislocation patterns during plastic deformation into consideration. Finally, we give an existence result for this model.