2006
DOI: 10.1007/s10450-006-0002-1
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Optimality Conditions for Infinite Order Hyperbolic Differential System

Abstract: In this paper, first, we establish the solvability of (n × n)-systems of hyperbolic type with inhomogeneous mixed Neumann conditions involving operator of infinite order. Using theorems of J. L. Lions, quadratic boundary control problem for this system is considered. The necessary and sufficient conditions for the optimality of the control is obtained and the set of inequalities that characterize these conditions is formulated. Finally, by applying the DubovitskiiMilyutin theorem of W. Kotarski, necessary and … Show more

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Cited by 4 publications
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“…References [14] [15] were among the first studies that presented the control problems of systems including infinite order operators. These problems were then extended in different ways, such as for higher system degrees [16] [17], and for parabolic and hyperbolic systems [14] [17] [18] [19] [20] [21].…”
Section: Introductionmentioning
confidence: 99%
“…References [14] [15] were among the first studies that presented the control problems of systems including infinite order operators. These problems were then extended in different ways, such as for higher system degrees [16] [17], and for parabolic and hyperbolic systems [14] [17] [18] [19] [20] [21].…”
Section: Introductionmentioning
confidence: 99%