On the Kneser property for reaction-diffusion equations in some unbounded domains with an H^{-1}-valued non-autonomous forcing term

Abstract

In this paper we prove the Kneser property for a reaction-diffusion equation on an unbounded domain satisfying the Poincaré inequality with an external force taking values in the space H^{−1}. Using this property of solutions we check also the connectedness of the associated global pullback attractor. We study also similar properties for systems of reaction-diffusion equations in which the domain is the whole R^N. Finally, the results are applied to a generalized logistic equation.