Banach空间中微分变分不等式系统的Bang-Bang准则

Abstract

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.

Key words: Differential variational inequalities, "Bang-Bang" principle, Density, KKM mapping

CLC Number:

O176.3

Cuiyun Shi,Maojun Bin. On the Bang-Bang Principle for Differential Variational Inequalities in Banach Spaces[J].Acta mathematica scientia,Series A, 2022, 42(6): 1653-1670.

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References 47

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

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