Semigrupo analítico e espaços de potência fracionária aplicados ao estudo das equações diferenciais.

Abstract

In this work we present an introduction to the Theory of Analytical Semigroups and Fractional Powers of Non-Limited Linear Operators. Next, we will see how this theory can be applied to determine the existence of solution to the following class of parabolic differential equations {(du/dt+Au=f (t,u (t)),&t>0.@u (0)= u0)┤

Where A : D (A) → X, with D (A) ư X, and f are given and meet certain conditions.