Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term | Zendy

Oleksiy V. Kapustyan | Zendy; Pavlo O. Kasyanov | Zendy; José Valero | Zendy

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Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term

Author(s) -

Oleksiy V. Kapustyan,

Pavlo O. Kasyanov,

José Valero

Publication year - 2014

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2014.34.4155

Subject(s) - attractor , uniqueness , term (time) , mathematics , manifold (fluid mechanics) , reaction–diffusion system , mathematical analysis , nonlinear system , set (abstract data type) , initial value problem , stable manifold , diffusion , physics , computer science , mechanical engineering , thermodynamics , quantum mechanics , engineering , programming language

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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