A Fixed Point Method for a Class of Nonlinear Evolution Systems Modeling a Mechanical Phenomenon

This paper deals with the study of a class of nonlinear evolution systems with parameter t which may interpreted as the time or the absolute temperature. Such type of problems arise in the study of quasistatic problem in viscoplasticity. The existence and uniqueness of the solution is obtained using standard arguments for elliptic equations followed by a xed point technique. The continuous dependence of the solution with respect to the data is also given. Finally, a mechanical example is presented in order to illustrate this result.