The trace triple for nonnegative solutions of the porous medium equation

Abstract

It is shown that, for every non-negative weak solution u of the generalized porous medium Eq. (1) $$\Psi (u)$$ takes a Radon measure as its lateral trace. When $$\Psi (u)$$ is integrable, u has an initial trace consisting of a bottom measure and a corner measure. The initial trace (bottom and corner measures) and the lateral trace form the trace triple for the solution. The initial-Dirichlet problem of prescribing trace triple is solved for the porous medium equation in the slow diffusion case.