Spatially periodic equilibria for a non local evolution equation

Saulo R.M. Barros; Antônio L. Pereira; Cláudio Possani; Adilson Simonis

doi:10.3934/dcds.2003.9.937

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2003, Volume 9, Issue 4: 937-948. Doi: 10.3934/dcds.2003.9.937

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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

Received: October 31, 2001

Revised: November 30, 2002

Published: June 2003

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Abstract

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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Mathematics Subject Classification: 45JO5, 45M05, 34C35, 34D45.

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