An inverse boundary value problem for the inhomogeneous porous medium equation

Abstract

In this paper we establish uniqueness in the inverse boundary value problem for the two coefficients in the inhomogeneous porous medium equation $\epsilon {\partial }_{t}u-\nabla \cdot (\gamma \nabla u^m)=0$, with $m>1$, in dimension 3 or higher, which is a degenerate parabolic type quasilinear PDE. Our approach relies on using a Laplace transform to turn the original equation into a coupled family of nonlinear elliptic equations, indexed by the frequency parameter ($1/h$ in our definition) of the transform. A careful analysis of the asymptotic expansion in powers of $h$, as $h\to \infty$, of the solutions to the transformed equation, with special boundary data, allows us to obtain sufficient information to deduce the uniqueness result.

References in corpus (3)

• Reconstruction for the coefficients of a quasilinear elliptic partial differential equation
• Enclosure method for the p-Laplace equation
• The Calderón inverse problem for isotropic quasilinear conductivities

Cited by in corpus (1)

• An inverse problem for the fractional porous medium equation