This award will support an international collaboration between Professor Jose Luis Menaldi of Wayne State University and Professors M.C. Bancora-Imbert, R. Gonzalez, and D. Tarzia of the Mathematical Institute "Beppo Levi" of the University of Rosario in Argentina. The collaborators will study three main research areas: i) Optimization problems with monotone controls; ii) Impulse control problems; and iii) Control problems with free boundaries. This class of problems has the property that they can be formulated in terms of (quasi) variational inequalities, and the investigators plan to solve them by using techniques from numerical analysis leading, in the process, not only to concrete algorithms but also to the study of rates of convergence and to numerical estimates. Optimization problems with monotone controls and impulse control problems arise from modeling the control of a dynamical system by an external force that, as a function of time, has jumps or other types of discontinuities. These models are quite useful in Operations Research and Economics. Other physical applications of monotone and impulse control methods originate in the study of oscillating systems and in the study of optimal allocation of resources. Likewise, the study of fluid flow through a porous medium, the theory of semiconductors, and the analysis of phase change problems, often lead to control problems with free boundaries, so that the class of problems under consideration is an important one with many practical applications. Furthermore, the project brings together active experienced collaborators with complementary skills to work on problems of mutual concern, and by so doing fulfills the objectives of the U.S.-Argentina Program. In addition, this award adds an international dimension to the U.S. PI's current support by the NSF Division of Mathematical Sciences through grant DMS8601998.
