A Functional Approach to Non-Autonomous Abstract Differential Equations: the Parabolic Case

Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

and

Dipartimento di Matematica
Universitá degli Studi di Trento
via Sommarive 14
38050 Povo (Trento), Italy

Abstract:

We give a functional approach to manage a class of Non-Autonomous Abstract Differential Equations, in the parabolic case, merging the theory of the Evolutionary Processes with the (Z)-A property defined by Desch and Schappacher. From here, results of existence and uniqueness derive in the classical way. As example we prove the existence for the solutions of a Fokker-Planck equation with non-local boundary conditions.