$Structure and regularity of the global attractor of a reaction-di{\S}usion equation with non-smooth nonlinear term$

Structure and regularity of the global attractor of a reaction-di{\S}usion equation with non-smooth nonlinear term

In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Kapustyan, Oleksiy V, Kasyanov, Pavlo O, Valero, José
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Analysis of PDEs Mathematics - Dynamical Systems
Online-Zugang:	Volltext bestellen
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. 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.
DOI:	10.48550/arxiv.1209.2010