A class of differential hemivariational inequalities constrained on nonconvex star-shaped sets

References

• Liu ZH, Zeng SD, Motreanu D. Evolutionary problems driven by variational inequalities. J Differ Equ. 2016;260(9):6787–6799.
   Web of Science ®Google Scholar
• Liu ZH, Zeng SD, Motreanu D. Partial differential hemivariational inequalities. Adv Nonlinear Anal. 2018;7(4):571–586.
   Web of Science ®Google Scholar
• Migórski S, Zeng SD. A class of differential hemivariational inequalities in banach spaces. J Glob Optim. 2018;72(4):761–779.
   Web of Science ®Google Scholar
• Panagiotopoulos PD. Non-convex superpotentials in the sense of fh clarke and applications. Mech Res Commun. 1981;8(6):335–340.
   Google Scholar
• Panagiotopoulos PD. Hemivariational inequalities. In: Hemivariational inequalities. Springer; 1993. p. 99–134.
   Google Scholar
• Bartosz K. Numerical methods for evolution hemivariational inequalities. In: Advances in variational and hemivariational inequalities. Springer; 2015. p. 111–144.
   Google Scholar
• Gasiński L, Liu ZH, Migórski S, et al. Hemivariational inequality approach to evolutionary constrained problems on star-shaped sets. J Optim Theory Appl. 2015;164(2):514–533.
   Web of Science ®Google Scholar
• Goeleven D. On the hemivariational inequality approach to nonconvex constrained problems in the theory of von kárman plates. J Appl Math Mech Z Angew Math Mech. 1995;75(12):861–866.
   Google Scholar
• Han JF, Lu L, Zeng SD. Evolutionary variational–hemivariational inequalities with applications to dynamic viscoelastic contact mechanics. Z Angew Math Phys. 2020;71(1):1–23.
   Web of Science ®Google Scholar
• Migórski S, Long FZ. Constrained variational-hemivariational inequalities on nonconvex star-shaped sets. Mathematics. 2020;8(10):1824.
   Web of Science ®Google Scholar
• Migórski S, Ochal A. Quasi-static hemivariational inequality via vanishing acceleration approach. SIAM J Math Anal. 2009;41(4):1415–1435.
   Web of Science ®Google Scholar
• Migórski S, Ochal A, Sofonea M. Nonlinear inclusions and hemivariational inequalities: models and analysis of contact problems. Vol. 26. New York (NY): Springer; 2012.
   Google Scholar
• Naniewicz Z. Hemivariational inequality approach to constrained problems for star-shaped admissible sets. J Optim Theory Appl. 1994;83(1):97–112.
   Web of Science ®Google Scholar
• Naniewicz Z, Panagiotopoulos PD. Mathematical theory of hemivariational inequalities and applications. Boca Raton: CRC Press; 1994.
   Google Scholar
• Peng ZJ. Optimal obstacle control problems involving nonsmooth cost functionals and quasilinear variational inequalities. SIAM J Control Optim. 2020;58(4):2236–2255.
   Web of Science ®Google Scholar
• Peng ZJ, Kunisch K. Optimal control of elliptic variational–hemivariational inequalities. J Optim Theory Appl. 2018;178(1):1–25.
   Web of Science ®Google Scholar
• Peng ZJ, Liu ZH, Liu XY. Boundary hemivariational inequality problems with doubly nonlinear operators. Math Ann. 2013;356(4):1339–1358.
   Web of Science ®Google Scholar
• Sofonea M, Migorski S. Variational-hemivariational inequalities with applications. . New York: Chapman and Hall/CRC; 2017.
   Google Scholar
• Sofonea M, Migórski S, Han WM. A penalty method for history-dependent variational–hemivariational inequalities. Comput Math Appl. 2018;75(7):2561–2573.
   Web of Science ®Google Scholar
• Aubin JP, Cellina A. Differential inclusions: set-valued maps and viability theory. Berlin: Springer; 2012.
   Google Scholar
• Pang JS, Stewart DE. Differential variational inequalities. Math Program. 2008;113(2):345–424.
   Web of Science ®Google Scholar
• Chen XJ, Wang ZY. Differential variational inequality approach to dynamic games with shared constraints. Math Program. 2014;146(1-2):379–408.
   Web of Science ®Google Scholar
• Liu ZH, Migórski S, Zeng SD. Partial differential variational inequalities involving nonlocal boundary conditions in banach spaces. J Differ Equ. 2017;263(7):3989–4006.
   Web of Science ®Google Scholar
• Liu ZH, Zeng SD. Penalty method for a class of differential variational inequalities. Appl Anal. 2021;100(7):1574–1589.
   Web of Science ®Google Scholar
• Lu L, Liu ZH, Motreanu D. Existence results of semilinear differential variational inequalities without compactness. Optimization. 2019;68(5):1017–1035.
   Web of Science ®Google Scholar
• Lu L, Liu ZH, Obukhovskii V. Second order differential variational inequalities involving anti-periodic boundary value conditions. J Math Anal Appl. 2019;473(2):846–865.
   Web of Science ®Google Scholar
• Nguyen TVA, Tran DK. On the differential variational inequalities of parabolic-elliptic type. Math Methods Appl Sci. 2017;40(13):4683–4695.
   Web of Science ®Google Scholar
• Li XW, Liu ZH. Sensitivity analysis of optimal control problems described by differential hemivariational inequalities. SIAM J Control Optim. 2018;56(5):3569–3597.
   Web of Science ®Google Scholar
• Liu ZH, Motreanu D, Zeng SD. Generalized penalty and regularization method for differential variational-hemivariational inequalities. SIAM J Optim. 2021;31(2):1158–1183.
   Web of Science ®Google Scholar
• Liu ZH, Zeng SD. Differential variational inequalities in infinite banach spaces. Acta Math Sci. 2017;37(1):26–32.
   Web of Science ®Google Scholar
• Lu L, Li LJ, Sofonea M. A generalized penalty method for differential variational-hemivariational inequalities. Acta Math Sci. 2022;42(1):247–264.
   Web of Science ®Google Scholar
• Zeng SD, Migórski S, Liu ZH. Well-posedness, optimal control, and sensitivity analysis for a class of differential variational-hemivariational inequalities. SIAM J Optim. 2021;31(4):2829–2862.
   Web of Science ®Google Scholar
• Peng ZJ, Gasiński L, Migórski S, et al. A class of evolution variational inequalities with nonconvex constraints. Optimization. 2019;68(10):1881–1895.
   Web of Science ®Google Scholar
• Faiz Z, Baiz O, Benaissa H, et al. Penalty method for a class of differential hemivariational inequalities with application. Numer Funct Anal Optim. 2021;42(10):1178–1200.
   Web of Science ®Google Scholar
• Clarke FH. Optimization and nonsmooth analysis. New York: SIAM; 1990.
   Google Scholar
• Zeidler E. Nonlinear functional analysis and its applications: II A/B. New York: Springer; 2013.
   Google Scholar
• Papageorgiou NS, Papalini F, Renzacci F. Existence of solutions and periodic solutions for nonlinear evolution inclusions. Rend Circ Mat Palermo. 1999;48(2):341–364.
   Google Scholar
• Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer; 1983.
   Google Scholar