Structure of the Global Attractor for Weak Solutions of a Reaction-Diffusion Equation

Authors

Oleksiy V. Kapustyan, Kyiv National Taras Shevchenko University, Kyiv, UkraineFollow
Pavlo O. Kasyanov, Institute for Applied System Analysis, National Technical University of Ukraine, Kyiv Polytechnic Institute, Kyiv, UkraineFollow
José Valero, Universidad Miguel Hernandez de Elche, Centro de Investigaci´on Operativa, Avda. Universidad s/n, 03202- Elche, SpainFollow

Author Country (or Countries)

Spain

Abstract

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.

Recommended Citation

V. Kapustyan, Oleksiy; O. Kasyanov, Pavlo; and Valero, José (2023) "Structure of the Global Attractor for Weak Solutions of a Reaction-Diffusion Equation," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/6