Optimal Controls in Flux, Source, and Initial Terms for Weakly Coupled Hyperbolic Systems

Abstract

In this paper, we prove the existence of an optimal control in flux-, source-, and initial terms for weakly coupled nonlinear hyperbolic systems. The basic idea for proving existence of an optimal control is to show first by parabolic regularization the existence of an entropy solution of the weakly coupled hyperbolic system for given control functions. Then, one has to show the stability of the entropy solution with respect to the control functions in order to get the optimal control.