On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces

Abstract

In this paper, we discuss a class of differential variational inequalities systems, which are obtained by semilinear evolution equations and generalized variational inequalities. At first, we consider the properties of solution set for generalized variational inequalities. Secondly, the existence results are shown by fixed point method for semilinear differential variational inequality. Our approaches are based on semigroup theory and fixed point theorem. Moreover, by using the density results, the nonlinear and infinite dimensional versions of the “bang-bang” principle for differential variational inequalities systems is derived. Also, an obstacle parabolic-elliptic system is given to illustrate the application of the obtained theory.