Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation

We study the relation between viscosity solutions and weak solutions of the equation $${\mathrm{\partial }}_t\left(\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u\right)=\mathrm{div}(\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{p-2}\mathrm{\nabla }u)\mathrm{.}$$ We prove that at least for non-negative functions these are equivalent concepts.