On some nonlinear evolution equations with the strong dissipation,II

In this paper we continue the existence theories of classical solutions of nonlinear evolution equations with the strong dissipation studied in a previous paper 5]. In particular, we give sufficient conditions under which some of the equations have global solutions and at the same time we find steady state solutions of these equations which are exponentially stable as t → ∞. In the application, we improve the existence results to the equations which describe a local statement of balance of momentum for materials for which the stress is related to strain and strain rate through some constitutive equation (cf. Greenberg et al. 6], Greenberg 7], Davis 2], Clements 1], etc.).