We consider a variant of Bouchaud's trap model on the one-dimensional lattice, on which a system of random walks evolve in a random environment and interact through a zero-range interaction. We prove that the density of particles, when properly rescaled, converges to the solution of the non-linear, non-homogeneous heat equation $u_t = \frac{d}{dW} \frac{d}{dx} (u+a u^2)$. In this equation, $\frac{d}{dW}$ is the Stieltjes derivative with respect to a realization of a two-sided subordinator $W$.
This is joint work with Freddy Hernandez (UFF, Brazil), Claudio Landim (IMPA, Brazil), and Augusto Teixeira (ENS, France).