ABSTRACT

I discuss three very different forward PDE problems which need data assimilation/inverse approaches to make them potentially useful in practical applications. The first problem is a reaction-diffusion system for biological transportation network formation and adaptation, the second is a highly nonstandard parabolic free boundary problem describing price formation in economic markets and the third problem is the incompressible Navier-Stokes-ForchheimerBrinkmann system for flow in porous media.