33,428 research outputs found
Optimal control of history-dependent evolution inclusions with applications to frictional contact
In this paper, we study a class of subdifferential evolution inclusions involving history-dependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example of an optimal control of a dynamic frictional contact problem in mechanics, whose weak formulation is the evolution variational inequality
Stability for a New Class of GNOVI with ( γ
By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions) with (γG,λ)-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained
Periodic solutions for a class of evolution inclusions
We consider a periodic evolution inclusion defined on an evolution triple of
spaces. The inclusion involves also a subdifferential term. We prove existence
theorems for both the convex and the nonconvex problem, and we also produce
extremal trajectories. Moreover, we show that every solution of the convex
problem can be approximated uniformly by certain extremal trajectories (strong
relaxation). We illustrate our results by examining a nonlinear parabolic
control system
Discrete Approximations of a Controlled Sweeping Process
The paper is devoted to the study of a new class of optimal control problems
governed by the classical Moreau sweeping process with the new feature that the polyhe-
dral moving set is not fixed while controlled by time-dependent functions. The dynamics of
such problems is described by dissipative non-Lipschitzian differential inclusions with state
constraints of equality and inequality types. It makes challenging and difficult their anal-
ysis and optimization. In this paper we establish some existence results for the sweeping
process under consideration and develop the method of discrete approximations that allows
us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type
sweeping process by their discrete counterparts
- …