Abstract
In this paper, we study the dynamical properties inside the global attractor for multivalued semiflows. Given a disjoint finite family of isolated weakly invariant sets, we prove, extending a previous result from the single-valued case, that the existence of a Lyapunov function, the property of being a dynamically gradient semiflow and the existence of a Morse decomposition are equivalent properties. We apply this abstract theorem to a reaction–diffusion inclusion.
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