Boundary value problems for semilinear evolution inclusions: Carathéodory selections approach

summary:In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions

Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics

We construct identities of Pohozhaev type, in the context of elastostatics and elastodynamics, by using the Noetherian approach. As an application, a non-existence result for forced semi-linear isotropic and anisotropic elastic systems is established