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Relaxation control for a class of evolution hemivariational inequalities

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Abstract

We consider a control system governed by a class of evolution hemivariational inequalities. The constraint on the control is given by a multivalued function with nonconvex values that is lower semicontinuous with respect to the state variable. Meanwhile, we handle the same system in which the constraint on the control is the upper semicontinuous convex valued regularization of the original constraint. We finally study relations between the solution sets of these systems.

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Author information

Authors and Affiliations

  1. College of Sciences, Guangxi University for Nationalities, Nanning, 530006, Guangxi Province, P. R. China

    Xiaoyou Liu & Zhenhai Liu

  2. School of Mathematical Science and Computing Technology, Central South University, Changsha, 410075, Hunan Province, P.R.China

    Xiaoyou Liu

  3. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis and College of Sciences, Guangxi University for Nationalities, Nanning, 530006, Guangxi Province, P. R. China

    Zhenhai Liu

Authors
  1. Xiaoyou Liu
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  2. Zhenhai Liu
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Correspondence to Xiaoyou Liu.

Additional information

Project supported by NNSF of China Grants Nos. 11271087 and 61263006.

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Liu, X., Liu, Z. Relaxation control for a class of evolution hemivariational inequalities. Isr. J. Math. 202, 35–58 (2014). https://doi.org/10.1007/s11856-014-1066-3

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  • DOI: https://doi.org/10.1007/s11856-014-1066-3

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