Spatially periodic equilibria for a non local evolution equation | Zendy

Saulo R.M. Barros | Zendy; Antônio Luíz Pereira | Zendy; Cláudio Possani | Zendy; Adilson Simonis | Zendy

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Spatially periodic equilibria for a non local evolution equation

Author(s) -

Saulo R.M. Barros,

Antônio Luíz Pereira,

Cláudio Possani,

Adilson Simonis

Publication year - 2003

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.2003.9.937

Subject(s) - attractor , evolution equation , constant (computer programming) , mathematics , work (physics) , space (punctuation) , mathematical physics , pure mathematics , mathematical analysis , partial differential equation , physics , thermodynamics , computer science , programming language , operating system

In this work we prove the existence of a global attractor for the non local evolution equation $ \frac { \partial m ( r , t ) } { \partial t } = - m ( r , t ) + \tanh ( \beta J $*$ m ( r , t ) ) $ in the space of $\tau$-periodic functions, for $\tau$ sufficiently large. We also show the existence of non constant (unstable) equilibria in these spaces.

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