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On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces
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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.
Title: On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces
Description:
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.
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