A class of evolution differential inclusion systems
- Авторы: Zhao J.1, Liu Z.2,3, Papageorgiou N.S.4
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Учреждения:
- Guangxi University of Finance and Economics
- Guangxi Minzu University
- Yulin Normal University
- Department of Mathematics, National Technical University of Athens
- Выпуск: Том 88, № 2 (2024)
- Страницы: 5-32
- Раздел: Статьи
- URL: https://journals.rcsi.science/1607-0046/article/view/254261
- DOI: https://doi.org/10.4213/im9450
- ID: 254261
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Аннотация
The main purpose of this paper is to study an abstract system which consists of a non-linear differential inclusion with $C_0$-semigroups and history-dependent operators combined with an evolutionary non-linear inclusion involvingpseudomonotone operators, which contains several interesting problems as special cases. We first introduce a hybrid iterative system by using the Rothe method, pseudomonotone operators theory,and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limiting procedure for solutions of the hybrid iterative system, we show that the existence of solutions to the original problem.
Об авторах
Jing Zhao
Guangxi University of Finance and Economics
Zhenhai Liu
Guangxi Minzu University; Yulin Normal Universityдоктор наук, профессор
Nikolaos S. Papageorgiou
Department of Mathematics, National Technical University of Athens
Email: npapg@math.ntua.gr
Список литературы
- M. Pierre, T. Suzuki, H. Umakoshi, “Global-in-time behavior of weak solutions to reaction-diffusion systems with inhomogeneous Dirichlet boundary condition”, Nonlinear Anal., 159 (2017), 393–407
- E. F. Keller, L. A. Segel, “Initiation of slime mold aggregation viewed as an instability”, J. Theoret. Biol., 26:3 (1970), 399–415
- K. Ishige, P. Laurencot, N. Mizoguchi, “Blow-up behavior of solutions to a degenerate parabolic-parabolic Keller–Segel system”, Math. Ann., 367:1-2 (2017), 461–499
- N. Mizoguchi, “Global existence for the Cauchy problem of the parabolic-parabolic Keller–Segel system on the plane”, Calc. Var. Partial Differential Equations, 48:3-4 (2013), 491–505
- N. Mizoguchi, “Type II blowup in a doubly parabolic Keller–Segel system in two dimensions”, J. Funct. Anal., 271:11 (2016), 3323–3347
- Wenxian Shen, Shuwen Xue, “Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on $mathbb R^N$”, Discrete Contin. Dyn. Syst., 42:6 (2022), 2893–2925
- Youshan Tao, Lihe Wang, Zhi-An Wang, “Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension”, Discrete Contin. Dyn. Syst. Ser. B, 18:3 (2013), 821–845
- А. Ф. Филиппов, Дифференциальные уравнения с разрывной правой частью, Наука, М., 1985, 224 с.
- Jong-Shi Pang, D. E. Stewart, “Differential variational inequalities”, Math. Program., 113:2 (2008), 345–424
- Xiaojun Chen, Zhengyu Wang, “Convergence of regularized time-stepping methods for differential variational inequalities”, SIAM J. Optim., 23:3 (2013), 1647–1671
- Xiaojun Chen, Zhengyu Wang, “Differential variational inequality approach to dynamic games with shared constraints”, Math. Program., 146:1-2 (2014), 379–408
- J. Gwinner, “On a new class of differential variational inequalities and a stability result”, Math. Program., 139:1-2 (2013), 205–221
- Lanshan Han, Jong-Shi Pang, “Non-Zenoness of a class of differential quasi-variational inequalities”, Math. Program., 121:1 (2010), 171–199
- Jong-Shi Pang, D. E. Stewart, “Solution dependence on initial conditions in differential variational inequalities”, Math. Program., 116:1-2 (2009), 429–460
- Jong-Shi Pang, Lanshan Han, G. Ramadurai, S. Ukkusuri, “A continuous-time linear complementarity system for dynamic user equilibria in single bottleneck traffic flows”, Math. Program., 133:1-2 (2012), 437–460
- Zhenhai Liu, Shengda Zeng, D. Motreanu, “Evolutionary problems driven by variational inequalities”, J. Differential Equations, 260:9 (2016), 6787–6799
- Zhenhai Liu, S. Migorski, Shengda Zeng, “Partial differential variational inequalities involving nonlocal boundary conditions in Banach spaces”, J. Differential Equations, 263:7 (2017), 3989–4006
- Zhenhai Liu, D. Motreanu, Shengda Zeng, “Nonlinear evolutionary systems driven by mixed variational inequalities and its applications”, Nonlinear Anal. Real World Appl., 42 (2018), 409–421
- Nguyen Van Loi, “On two-parameter global bifurcation of periodic solutions to a class of differential variational inequalities”, Nonlinear Anal., 122 (2015), 83–99
- Liang Lu, Zhenhai Liu, V. Obukhovskii, “Second order differential variational inequalities involving anti-periodic boundary value conditions”, J. Math. Anal. Appl., 473:2 (2019), 846–865
- Zhenhai Liu, Shengda Zeng, D. Motreanu, “Partial differential hemivariational inequalities”, Adv. Nonlinear Anal., 7:4 (2018), 571–586
- Xiuwen Li, Zhenhai Liu, “Sensitivity analysis of optimal control problems described by differential hemivariational inequalities”, SIAM J. Control Optim., 56:5 (2018), 3569–3597
- Zhenhai Liu, D. Motreanu, Shengda Zeng, “Generalized penalty and regularization method for differential variational-hemivariational inequalities”, SIAM J. Optim., 31:2 (2021), 1158–1183
- Shengda Zeng, Zhenhai Liu, S. Migorski, “A class of fractional differential hemivariational inequalities with application to contact problem”, Z. Angew. Math. Phys., 69:2 (2018), 36, 23 pp.
- Shengda Zeng, S. Migorski, Zhenhai Liu, “Well-posedness, optimal control, and sensitivity analysis for a class of differential variational-hemivariational inequalities”, SIAM J. Optim., 31:4 (2021), 2829–2862
- S. Migorski, Shengda Zeng, “A class of differential hemivariational inequalities in Banach spaces”, J. Global Optim., 72:4 (2018), 761–779
- S. Migorski, “A class of history-dependent systems of evolution inclusions with applications”, Nonlinear Anal. Real World Appl., 59 (2021), 103246, 21 pp.
- Nguyen Thi Van Anh, Tran Dinh Ke, “On the differential variational inequalities of parabolic-parabolic type”, Acta Appl. Math., 176 (2021), 5, 25 pp.
- Xiuwen Li, Zhenhai Liu, N. S. Papageorgiou, “Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications”, Nonlinearity, 36:2 (2023), 1323–1348
- Yongjian Liu, Zhenhai Liu, N. S. Papageorgiou, “Sensitivity analysis of optimal control problems driven by dynamic history-dependent variational-hemivariational inequalities”, J. Differential Equations, 342 (2023), 559–595
- Shouchuan Hu, N. S. Papageorgiou, Handbook of multivalued analysis, v. I, Math. Appl., 419, Theory, Kluwer Acad. Publ., Dordrecht, 1997, xvi+964 pp.
- Shouchuan Hu, N. S. Papageorgiou, Handbook of multivalued analysis, v. II, Math. Appl., 500, Applications, Kluwer Acad. Publ., Dordrecht, 2000, xii+926 pp.
- S. Migorski, A. Ochal, “Quasi-static hemivariational inequality via vanishing acceleration approach”, SIAM J. Math. Anal., 41:4 (2009), 1415–1435
- S. Migorski, A. Ochal, M. Sofonea, Nonlinear inclusions and hemivariational inequalities. Models and analysis of contact problems, Adv. Mech. Math., 26, Springer, New York, 2013, xvi+285 pp.
- Z. Denkowski, S. Migorski, N. S. Papageorgiou, An introduction to nonlinear analysis: theory, Kluwer Acad. Publ., Boston, MA, 2003, xvi+689 pp.
- P. Kalita, “Convergence of Rothe scheme for hemivariational inequalities of parabolic type”, Int. J. Numer. Anal. Model., 10:2 (2013), 445–465
- Xunjing Li, Jiongmin Yong, Optimal control theory for infinite dimensional systems, Systems Control Found. Appl., Birkhäuser Boston, Inc., Boston, MA, 1995, xii+448 pp.
- H. F. Bohnenblust, S. Karlin, “On a theorem of Ville”, Contributions to the theory of games, Ann. of Math. Stud., 24, Princeton Univ. Press, Princeton, NJ, 1950, 155–160
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Appl. Math. Sci., 44, Springer-Verlag, New York, 1983, viii+279 pp.
- Zijia Peng, Zhenhai Liu, Xiaoyou Liu, “Boundary hemivariational inequality problems with doubly nonlinear operators”, Math. Ann., 356:4 (2013), 1339–1358
- Yongjian Liu, Zhenhai Liu, Sisi Peng, Ching-Feng Wen, “Optimal feedback control for a class of fractional evolution equations with history-dependent operators”, Fract. Calc. Appl. Anal., 25:3 (2022), 1108–1130
- Biao Zeng, Zhenhai Liu, “Existence results for impulsive feedback control systems”, Nonlinear Anal. Hybrid Syst., 33 (2019), 1–16
- Zhao Jing, Zhenhai Liu, E. Vilches, Chingfeng Wen, Jen-Chih Yao, “Optimal control of an evolution hemivariational inequality involving history-dependent operators”, Commun. Nonlinear Sci. Numer. Simul., 103 (2021), 105992, 17 pp.
- E. Maitre, P. Witomski, “A pseudo-monotonicity adapted to doubly nonlinear elliptic-parabolic equations”, Nonlinear Anal., 50:2 (2002), 223–250
- Weimin Han, M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity, AMS/IP Stud. Adv. Math., 30, Amer. Math. Soc., Providence, RI; International Press, Somerville, MA, 2002, xviii+442 pp.
- M. Sofonea, Weimin Han, M. Shillor, Analysis and approximation of contact problems with adhesion or damage, Pure Appl. Math. (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2006, xviii+220 pp.