In this paper we study discrete approximations of continuous-time evolution systems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "broken lines." This result allows us to establish the value and strong solution convergences of discrete approximations of the Bolza problem for constrained infinite-dimensional differential/evolution inclusions under natural assumptions on the initial data.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
49J52, 49M25, 90C30
Mordukhovich, Boris S., "Discrete Approximations of Differential Inclusions in Infinite-Dimensional Spaces" (2005). Mathematics Research Reports. 31.