Electron. J. Diff. Equ., Vol. 2010(2010), No. 138, pp. 1-12.

Existence and upper semicontinuity of global attractors for neural fields in an unbounded domain

Severino Horacio da Silva

Abstract:
In this article, we prove the existence and upper semicontinuity of compact global attractors for the flow of the equation
$$ \frac{\partial u(x,t)}{\partial t}=-u(x,t)+ J*(f\circ u)(x,t)+ h, \quad h > 0, $$
in $L^{2}$ weighted spaces.

Submitted March 16, 2010. Published September 27, 2010.
Math Subject Classifications: 45J05, 45M05, 34D45.
Key Words: Well-posedness; global attractor; upper semicontinuity of attractors.

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Severino Horácio da Silva
Unidade Acadêmica de Matemática e Estatística UAME/CCT/UFCG
Rua Aprígio Veloso, 882, Bairro Universitário CEP 58429-900
Campina Grande-PB, Brasil
email: horacio@dme.ufcg.edu.br

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