Existência de soluções de equilíbrios tipo Instanton para uma equação de evolução com convolução.

Abstract

In this work we prove existence and uniqueness of solution for the Cauchy problem corresponding to nonlocal evolution equation (Download file to see the equation). We exhibit an energy functional associated to this equation, and verify that it satisfies the Lyapunov property. Moreover, use this function to show the existence and local stability of a equilibrium solution reported in the literature as instanton.