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 paper is devoted to the stable method for ill-posed variational inequalities in mechanics. As examples of such variational inequalities we can consider four problems.
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.
文摘The paper is devoted to the stable method for ill-posed variational inequalities in mechanics. As examples of such variational inequalities we can consider four problems.
