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.
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Günther Grün, Degenerate Parabolic Differential Equations of Fourth Order and a Plasticity Model with Non-Local Hardening. Z. Anal. Anwend. 14 (1995), no. 3, pp. 541–574DOI 10.4171/ZAA/639