Rothe approach to the existence of solution of an ablation-transpiration cooling control system

A one dimensional ablation model with transpiration cooling control and nonlinear effect is studied, which is a distributed parameter control system with moving boundary and both governing equation and boundary conditions involving control variable. A solution is given by a Rothe approximation scheme.

Optimality conditions for systems with insufficient data

In this paper we use the Dubovitski–Milyutin formalism to establish necessary and sufficient conditions for optimality in a nonlinear, distributed parameter control system, with convex cost criterion and initial condition not given a priori (that is it is not a known function but instead it belongs to a specified set). Our result extends a recent theorem of Lions. Finally a concrete example is worked out in detail.