Algumas propriedades de equações diferenciais em espaços de Banach e aplicações a campos neurais.

Abstract

In this work we study some properties of abstract differential equations in Banach spaces and we apply the results for study the non local evolution equation of neural fields @u(x; t) @t = �����u(x; t) + J (f u)(x; t) + h; h > 0; in the phase space L2(S1): We prove that this equation generates one C1 flow, and we show the existence of a global attractor for this flow.