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Monotone Method for Equations Describing Transport Phenomena in a Banach Space

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Monotone Method for Equations Describing Transport Phenomena in a Banach Space

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Title: Monotone Method for Equations Describing Transport Phenomena in a Banach Space
Author: Vatsala, A. S.; Pachpatte, B. G.
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).
URI: http://hdl.handle.net/10106/2419
Date: 1981-06

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