This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a f...This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.展开更多
The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation...The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.展开更多
In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the ...In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.展开更多
基金supported by the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NNSF of China(12371312)+1 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the project cooperation between Guangxi Normal University and Yulin Normal University.
文摘This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
基金received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement(823731-CONMECH)supported by the National Science Center of Poland under Maestro Project(UMO-2012/06/A/ST1/00262)+3 种基金National Science Center of Poland under Preludium Project(2017/25/N/ST1/00611)supported by the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland(3792/GGPJ/H2020/2017/0)Qinzhou University Project(2018KYQD06)National Natural Sciences Foundation of Guangxi(2018JJA110006)
文摘The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is established under some suitable assumptions.
基金The first author was supported by the Guangxi Natural Science Foundation of China(Grant No.2021GXNSFFA196004)National Natural Science Foundation of China(Grant No.12001478)+4 种基金Horizon 2020 of the European Union(Grant No.823731 CONMECH)National Science Center of Poland(Grant No.2017/25/N/ST1/00611)The second author was supported by National Science Foundation of USA(Grant No.DMS 1720067)The third author was supported by the National Science Center of Poland(Grant No.2021/41/B/ST1/01636)the Ministry of Science and Higher Education of Poland(Grant Nos.4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019)。
文摘In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.
