Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 42, pp. 1-9.

Title: Properties of an equation for neural fields in a bounded domain

Author: Severino Horacio da Silva (FCG, Campina Grande - PB, Brasil)

Abstract:
 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.