This research program investigates the competition between dissipative mechanisms such as frictions and the destabilizing action of nonlinearity of the material response. The corresponding nonlinear evolution (partial differential) equations exhibit both hyperbolic and parabolic characters. Their analysis for the qualitative behavior of the physical system poses new and difficult mathematical problems. Specific results from the research program are expected to provide insight to physical problems such as shear band formation for strain-rate dependent materials and the motion of viscoelastic materials with fading memory.
