Nonhomogeneous initial-boundary value problems for coercive and self-controlling models of monotone type

Based on the idea of partial Yosida approximation we prove global in time e xistence of nonhomogeneous initial-boundary value problems for the class of coercive models of monotone type from the theory of inelastic deformations of metals. Then using this result and the coercive limits idea introduced in [8], we approximate self-controlling problems with nonhomogeneous bounda ry data by a sequence of coercive models and prove a convergence result.