This award supports Professors H. T. Banks, K. Ito and C. Wang of the University of Southern California to continue their collaboration in applied mathematics research with Professor F. Kappel and others of the University of Graz and K. Kunisch of the Technical University of Graz, Austria. They share interests in control theory that focus on the problems of estimating parameters in partial differential equations from known observation of a given process and also the approximation of functional and partial differential equations stressing applications to control and inverse problems. The specific topics on which they will work include modeling and parameter estimation techniques in size/age structured population models, the identifiability of parameters in models of visco-elastic systems, and the development of an approximation framework for nonlinear dynamics in a Banach space setting. These U.S. and Austrian mathematicians have been among the leaders in the development of methods and applications in a wide variety of problems in optimization, approximation and parameter estimation for functional and partial differential equations. Their productive collaboration has already resulted in numerous publications containing applications to meaningful physical and biological problems. The proposed work promises to continue this contribution by focusing on technically interesting problems with relevance to mechanics and population dynamics.
