  In this paper we establish uniqueness in the inverse boundary value problem
for the two coefficients in the inhomogeneous porous medium equation
$\epsilon\partial_tu-\nabla\cdot(\gamma\nabla u^m)=0$, 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.
