Nonautonomous initial-boundary value problems in the viscoplasticity theory

Abstract

We prove existence of a solution to the nonautonomous, noncoercive, quasistatic models in the viscoplasticity theory. This extends the results shown earlier by the author in Math. Methods Appl. Sci. 27 (2004), 1347–1365 and Math. Methods Appl. Sci. 31 (2008), 775–792, for the autonomous case. As a special case we obtain existence of the solution to the nonautonomous kinematic hardening model, where the constitutive nonlinearity has a polynomial or a rapid growth at infinity.