Evolutionary quasi-variational and variational inequalities with constraints on the derivatives

Abstract

This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type, but are not required to be coercive for the existence of weak solutions, which is obtained by a double penalization/regularization for the approximation of the solutions. In the case of time-dependent convex sets that are independent of the solution, we show also the uniqueness and the continuous dependence of the strong solutions of the variational inequalities, extending previous results to a more general framework.

Keywords

• evolutionary quasi-variational inequalities
• gradient constraints
• constraints on the derivatives
• 35r35
• 35k87
• 35k92
• 47j20
• 49j40