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Hemivariational Inequality Approach to Evolutionary Constrained Problems on Star-Shaped Sets

Author

Listed:
  • Leszek Gasiński

    (Jagiellonian University)

  • Zhenhai Liu

    (College of Sciences, Guangxi University for Nationalities)

  • Stanisław Migórski

    (Jagiellonian University)

  • Anna Ochal

    (Jagiellonian University)

  • Zijia Peng

    (College of Sciences, Guangxi University for Nationalities)

Abstract

In this paper, we consider a nonconvex evolutionary constrained problem for a star-shaped set. The problem is a generalization of the classical evolution variational inequality of parabolic type. We provide an existence result; the proof is based on the hemivariational inequality approach, a surjectivity theorem for multivalued pseudomonotone operators in reflexive Banach spaces, and a penalization method. The admissible set of constraints is closed and star-shaped with respect to a certain ball; this allows one to use a discontinuity property of the generalized Clarke subdifferential of the distance function. An application of our results to a heat conduction problem with nonconvex constraints is provided.

Suggested Citation

  • Leszek Gasiński & Zhenhai Liu & Stanisław Migórski & Anna Ochal & Zijia Peng, 2015. "Hemivariational Inequality Approach to Evolutionary Constrained Problems on Star-Shaped Sets," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 514-533, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0587-6
    DOI: 10.1007/s10957-014-0587-6
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    Cited by:

    1. Zijia Peng & Karl Kunisch, 2018. "Optimal Control of Elliptic Variational–Hemivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 1-25, July.
    2. Stanisław Migórski & Long Fengzhen, 2020. "Constrained Variational-Hemivariational Inequalities on Nonconvex Star-Shaped Sets," Mathematics, MDPI, vol. 8(10), pages 1-18, October.

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