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

Jos\'e Valero; Oleksiy V. Kapustyan; Pavlo O. Kasyanov

arxiv: 1209.2010 · v1 · pith:ZSPYMGTJnew · submitted 2012-09-10 · 🧮 math.DS · math.AP

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

Oleksiy V. Kapustyan , Pavlo O. Kasyanov , Jos\'e Valero This is my paper

classification 🧮 math.DS math.AP

keywords attractorglobalequationstructureusionboundedcasecauchy

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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.

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

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