Discussiones Mathematicae Differential Inclusions 19 (1999) 67-84
School of Information Technology and Engineering
and Department of Mathematics, University of Ottawa
In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.
Keywords: dynamic models, unitary group, semigroup, differential inclusions, vibration, optimal flow rate.
1991 Mathematics Subject Classification: 34K20, 35Q72, 93D05, 93D20.
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Received 12 July 1999