Characterization of the attractor for nonautonomous reaction-di¤usion equations with discontinuous nonlinearity

Abstract

In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-di¤usion equation with a discontinuous nonlinearity. We obtain rst several properties concerning the uniqueness and regularity of non-negative so- lutions. 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 semi ow attractors.