Spatially periodic equilibria for a non local evolution equation

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July 2003, 9(4): 937-948. doi: 10.3934/dcds.2003.9.937

Spatially periodic equilibria for a non local evolution equation

Saulo R.M. Barros ^1, , Antônio L. Pereira ^1, , Cláudio Possani ^1, and Adilson Simonis ^1,

1.	Instituto de Matemática e Estatística, Universidade de São Paulo, R. do Matão 1010, 05508-900, S. Paulo, Brazil, Brazil, Brazil, Brazil

Received November 2001 Revised December 2002 Published April 2003

Abstract
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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.

Keywords: Ising spin system, global attractor, numerical results., stationary solutions, periodic equilibria.

Mathematics Subject Classification: 45JO5, 45M05, 34C35, 34D4.

Citation: Saulo R.M. Barros, Antônio L. Pereira, Cláudio Possani, Adilson Simonis. Spatially periodic equilibria for a non local evolution equation. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 937-948. doi: 10.3934/dcds.2003.9.937

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