Sufficient Conditions of Optimality for Second Order Differential Inclusions
Gulgun Kayakutlu,
Elimhan N. Mahmudov
Issue:
Volume 1, Issue 1, December 2017
Pages:
1-6
Received:
12 December 2016
Accepted:
21 December 2016
Published:
16 January 2017
DOI:
10.11648/j.engmath.20170101.11
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Abstract: In this paper we are concerned with the Bolza problem (PC) for second order differential inclusions (SODIs). The aim is to derive sufficient conditions of optimality for a problem (PC). The basic concept of obtaining these conditions is the locally adjoint mappings (LAMs). Besides the transversality conditions, approaches to the general problem therefore involve distinctive Euler-Lagrange and Hamiltonian kind of adjoint inclusions. Furthermore, the aim of the considered “linear” problem with SODIs is to show the reader, by example, how the obtained results can be applied in practice.
Abstract: In this paper we are concerned with the Bolza problem (PC) for second order differential inclusions (SODIs). The aim is to derive sufficient conditions of optimality for a problem (PC). The basic concept of obtaining these conditions is the locally adjoint mappings (LAMs). Besides the transversality conditions, approaches to the general problem the...
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A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels
Marie Sjiernquist Desatnik,
Raad Yahya Qassim
Issue:
Volume 1, Issue 1, December 2017
Pages:
7-10
Received:
1 June 2017
Accepted:
22 June 2017
Published:
27 July 2017
DOI:
10.11648/j.engmath.20170101.12
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Abstract: One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.
Abstract: One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel ...
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