Gap functions and global error bounds for differential variational-hemivariational inequalities. (English) Zbl 1516.49006
Summary: This paper concerns with the study of a differential variational-hemivariational inequality (DVHVI, for short) in infinite-dimensional Banach spaces. We first introduce the new concept of gap functions for the variational control system of (DVHVI). Then, we consider two kinds of gap functions which are regularized gap function and Moreau-Yosida regularized gap function, respectively, and examine the relevant properties of the gap functions. Moreover, two global error bounds which depend implicitly on the regularized gap function and the Moreau-Yosida regularized gap function, accordingly, are obtained. Finally, in order to illustrate the applicability of the theoretical results, we investigate a coupled dynamic system which is formulated by a nonlinear reaction-diffusion equation described by a time-dependent nonsmooth semipermeability problem.
Keywords:
differential variational-hemivariational inequality; gap function; Moreau-Yosida regularized gap function; global error bound; nonlinear reaction-diffusion equation; semipermeability problemReferences:
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