In this paper we study the structure of the global attractor for a multivalued semiflow generated by weak solutions of a reaction-diffusion equation in which uniqueness of the Cauchy problem is not guaranteed, improving the results of a previous paper. Under suitable assumptions, we prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one but considering in this last case only solutions in the set of bounded complete trajectories.
V. Kapustyan, Oleksiy; O. Kasyanov, Pavlo; and Valero, José
"Structure of the Global Attractor for Weak Solutions of a Reaction-Diffusion Equation,"
Applied Mathematics & Information Sciences: Vol. 09:
5, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/6