Electron. J. Diff. Equ., Vol. 2012 (2012), No. 42, pp. 1-9.

Properties of an equation for neural fields in a bounded domain

Severino Horacio da Silva

In this work we study the global dynamics of an evolution equation for neural fields, where the flow generated by this equation in the phase space $L^2(S^1)$, is $C^1$. Furthermore we exhibit a continuous Lyapunov functional and use it for proving that this flow has the gradient property.

Submitted March 28, 2011. Published March 16, 2012.
Math Subject Classifications: 45J05, 45M05, 37B25.
Key Words: Well-posedness; smooth orbit; gradient flow.

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Severino Horácio da Silva
Unidade Acad&ecric;mica de Matemática e Estatíistica UAME/CCT/UFCG
Rua Apríigio Veloso, 882, Bairro Universitário CEP 58429-900
Campina Grande - PB, Brasil
email: horaciousp@gmail.com; horacio@dme.ufcg.edu.br

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