On the solution set of nonconvex subdifferential evolution inclusions
نویسندگان
چکیده
منابع مشابه
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type
In this paper we consider nonconvex evolution inclusions driven by time dependent convex subdifferentials. First we establish the existence of a continuous selection for the solution multifunction and then we use that selection to show that the solution set is path connected. Two examples are also presented.
متن کاملNonconvex Evolution Inclusions Generated by Time - Dependent Subdifferential Operators
We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials 0(t,x) without assuming that (t,.) is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover,r we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path-connected in C(T,H). These result...
متن کاملEvolution inclusions of the subdifferential type depending on a parameter
In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S(λ) is both Vietoris and Hausdorff metric continuous in λ ∈ Λ. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
متن کاملParametrized Relaxation for Evolution Inclusions of the Subdifferential Type
In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdiierentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the \Filippov-Gronwall" inequality and using it, we prove the par...
متن کاملOn the Structure of the Solution Set of Evolution Inclusions with Time{dependent Subdifferentials
In this paper we consider evolution inclusions driven by a time dependent subdifferential operator and a set-valued perturbation term. First we show that the problem with a convex-valued, h∗-u.s.c. orientor field (i.e. perturbation term) has a nonempty solution set which is an Rδ-set in C(T,H), in particular then compact and acyclic. For the non convex problem (i.e. the orientor field is non co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1994
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1994.128477