Partial Differential Equations with Infinite Delay Existence Approximation and Stability in Frechet Spaces

Abstract

In this thesis, we prove existence of a solutions to non-linear differential equations with infinite delay in Banach spaces. We construct a space and the unique solutions are given by semigroups in this space. Applications to Partial Differential Equations with infinite delay are given. Further, we show that the semigroup on the chet space is approximated by a sequence of semi-groups defined on Banach spaces. This sequence of semigroups give solutions of finite delay differential equations. In addition the existence result is extended to neutral delay equations. By generalizing the notion of limit dynamical system on uniform spaces, we show that an orbit which is bounded in a Banach space is relatively compact in the limit dynamical system corresponding to the space. Using this we show existence of invariant sets.