University of Heidelberg, Applied Analysis Seminar
Thu 02.06.2022
14:15, posted in Applied Analysis
Dr. Tuhin Ghosh (Bielefeld University)
Inverse problem for the porous medium equation
Seminar Room 2

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.

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