Monotone Method for Equations Describing Transport Phenomena in a Banach Space
Abstract
**Please note that the full text is embargoed** ABSTRACT: Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach
space has been recently considered in [2,7] by utilizing monotone iterative method.
A special type of B.V.P. of the form [see pdf for notation] in finite dimensional spaces have been recently investigated in [6].
It is of interest to investigate (1.1) in a Banach space since special forms of them occur in transport processes [1,8,9].
In order to develop monotone technique for (1.1) it becomes necessary to develop a comparison Theorem
(see Theorem 2.1) which is of interest in itself. The advantage of using monotone iterative technique to such equations is
that the iterates are solutions of linear initial value problems which are easily computable. In this paper we develop monotone
technique for (1.1).