Jiaohui Xu, Tomás Caraballo (Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla) and José Valero (Centro de Investigación Operativa, Universidad Miguel Hernandez de Elche)
Abstract: In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is different from ones used in the previous published literature on the long time behavior of heat equations with memory, which is carried out by the Dafermos transformation. As a consequence, the obtained results provide complete information about the attracting sets for the original problem, instead of the transformed one. In particular, the proved results also generalize and complete previous literature in the local case.