Abstract:
In this talk, we will discuss the inverse boundary value problem associated with the porous medium equation (PME): $\epsilon \partial_t u(t,x) − \nabla\cdot (\gamma \nabla u^m(t,x)) = 0, with m > 1. As its name suggests, the PME can be seen as a model for the flow of a gas through a porous medium, with the function $u(t, x)$ being the density of the gas at time $t$ and position $x$. The parameters $\epsilon$ and $\gamma$ then depend on the particular gas considered, and also on the properties of the medium. It is a degenerate nonlinear parabolic PDE, also used as a model for phenomena in fields such as plasma physics, and population dynamics. Here we will present a discussion about the unique recovery of the parameters from the relevant boundary Cauchy data.