Extremal bounded complete trajectories for nonautonomous reaction–diffusion equations with discontinuous forcing term (2019), Revista Matemática Complutense: 1-35

Tomás Caballero (The University of Sevilla), José A. Langa(University of Sevilla) and José Valero (University Miguel Hernández of Elche).

Abstract.In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term of Heaviside type. Using this principle, we study the structure of the global attractor in both the autonomous and nonautonomous cases. In particular, in the last case we prove that the pullback attractor is confined between two special bounded complete trajectories, which play the role of nonautonomous equilibria.

Keywords.  Differential inclusions; Reaction–diffusion equations; Pullback attractors; Nonautonomous dynamical systems; Multivalued dynamical systems; Structure; Comparison of solutions.