Optimal solutions for a free boundary problem for crystal growth
Pekka Neittaanmäki, Thomas I. Seidman · 1989
. We consider a free boundary problem modeling the growth/dissolution of a crystal in a radially symmetric setting. Existence of an optimal boundary control, minimizing a cost functional of a standard `integral-quadratic' form, is already known and we here consider the characterization and computation of such an optimal control. 1. Introduction In [7] an existence proof was given for an optimal boundary control minimizing a fairly standard sort of cost functional J with dynamics given by a free boundary problem corresponding to a model of growth (dissolution) of a radially symmetric crystal grain. Our present concerns are: the development of the corresponding optimality conditions, with some consequent additional regularity, and also the computational aspects of the optimization. Consider a solution of some substance surrounding a `crystal grain' of the pure material. Letting\\Omega = \\Omega\\Gamma t) be the (bounded) spatial region in IR d occupied by the solution, we assume that the...