  In this paper, we study the asymptotic behavior of the solutions of a
nonautonomous differential inclusion modeling a reaction-diffusion equation
with a discontinuous nonlinearity. We obtain first several properties
concerning the uniqueness and regularity of non-negative solutions. Then we
study the structure of the pullback attractor in the positive cone, showing
that it consists of the zero solution, the unique positive nonautonomous
equilibrium and the heteroclinic connections between them, which can be
expressed in terms of the solutions of an associated linear problem. Finally,
we analyze the relationship of the pullback attractor with the uniform, the
cocycle and the skew product semiflow attractors.
