In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set is both Vietoris and Hausdorff metric continuous in . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where is the pseudo-Laplacian operator.
In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem")....
Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell’equazione di evoluzione non autonoma , con il dato iniziale , in spazi di Banach. I dominii degli operatori variano in e non sono necessariamente densi in . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità holderiana della soluzione e della sua derivata.
In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.