# American Institute of Mathematical Sciences

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

## Spatially periodic equilibria for a non local evolution equation

 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

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