In this talk I will use a classic moving boundary problem of fluid dynamics to offer some insight into the kind of questions and results researchers in nonlinear partial differential equations are interested in.
I will discuss some situations when uncertainty in model parameters motivates modeling in terms of random functions. Moreover, some about what is involved in the analysis of such problems. In the first example I consider a problem in mathematical finance, while in the second I consider a problem regarding waves propagating through very complex media.
