Geodesic
Solution representation for a linear gas flow model in pipeline
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2017), pp. 27-37.

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The canonical system formed the eigenfunctions and associated eigenfunctions for the underlying operator and the adjoint operator is obtained for the linear partial differential equations generating by transient gas flow in pipeline. The new multi-parametric integral transformations for the space variable based on the given canonical system are introduced which together Laplace transformation with respect to the time variable turn the initial boundary value problems into algebraic equations in the frequency domain. Also, the inverse multi-parametric integral transformations are given on the base of which the solution of the considered problem can be represented in the original variables.
Keywords: linear partial differential equations; multi-parametric integral transformations; frequency domain. 
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M. P. Dymkov. Solution representation for a linear gas flow model in pipeline. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2017), pp. 27-37. http://geodesic.mathdoc.fr/item/BGUMI_2017_3_a3/

[1] V. Dymkou, R. Rabenstein, P. Stefen, “Discrete simulation of a class of distributed systems using functional analytic methods”, Multidimens. Syst. Signal Process, 17 (2006), 177–209 | DOI | MR | Zbl

[2] M. Dymkov, V. Dymkou, “Multifunctional transformation method in gas pipelines modeling”, Eruginskie chteniya – 2013: XV Mezhdunar. nauch. konf. po diff. uravneniyam (Grodno). Institut matematiki NAN Belarusi, 2 (2013), 83

[3] V. Dymkou, A. Poherat, “Spectral methods for wall bounded MHD”, J. Theor. Comput. Fluid Dyn, 23 (2009), 535–555 | DOI | Zbl

[4] A. Osiadacz, “Simulation and analysis of gas network”, London : Gulf Publishing Company, 1987

[5] H. Aalto, “Real-time receding horizont optimization of gas pipeline networks”, [Electronic resource], 2005 | DOI | Zbl

[6] D. Khenri, “Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii: per. s angl.”, Mir, 1985