Dynamic projection operator method in the theory of hyperbolic systems of partial differential equations with variable coefficients

• Autorzy: Leble S. , Vereshchagina I.

Identyfikatory

DOI

10.17466/tq2017/21.2/s

• Języki publikacji: EN

Abstrakty

EN

We consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients. It is supposed that the dependence of coefficients on the only variable χ is weak, that is described by the introduction of a small parameter. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics in waveguides with a variable cross-section. Projection operators are constructed for the Cauchy problem to fix unidirectional modes. The method of successive approximations (perturbation theory) is developed and based on the pseudodifferential operators theory. The application of projection operators adapted for the case under consideration allows deriving approximate evolution equations corresponding to the separated directed waves.

Słowa kluczowe

EN

hyperbolic PDE; idempotents; inhomogeneous media; acoustics

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2017
• Tom: Vol. 21, No 2
• Strony: 109--120
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Leble S.

• Immanuel Kant Baltic Federal University, Nevskogo 14, 236004 Kaliningrad, Russia

autor

Vereshchagina I.

• Immanuel Kant Baltic Federal University, Nevskogo 14, 236004 Kaliningrad, Russia

Bibliografia

• [1] Chu B T and Kovasznay L S G 1958 J. Fluid. Mech. 3 (05)
• [2] Vereshchagina I 1980, diploma thesis under S. Leble supervision, Kaliningrad State University
• [3] Bessarab F, Kshevetsky S and Leble S 1984 Theses of conf. Use of Modern Phys. Methods in Nondestructing Control 144
• [4] Leble S B 1991 Nonlinear Waves in Waiveguides with Stratification, Springer
• [5] Perelomova A A 1998 Acta Acustica 84 (6) 1002
• [6] Perelomova A A 2000 Applied Mathematics Letters 13 93
• [7] Pierce A 2002 Nonlinear Acoustics in the Beginning of the 21st Century Rudenko O V and Sapozhnikov O A Eds. 1 11
• [8] Perelomova A A 2001 Acta Acustica 87 176
• [9] Perelomova A A 2003 Acta Acustica united with Acustica 89 754
• [10] Perelomova A A 2006 Physics Letters A 357 42
• [11] Peradzinski Z 1971 Bull. Acad. Polon. Sci. 19 717
• [12] Zaitsev A and Leble S 1987 New method in nonlinear waves theory, Kaliningrad State University, Kaliningrad (in Russian)
• [13] Kuszner M and Leble S 2011 J. Phys. Soc. Jpn. 80 24002
• [14] Kinsler P 2010 Phys. Rev. A 81 23808
• [15] Kuszner M and Leble S 2013 J. Phys. Soc. Jpn.
• [16] Belov V V, Dobrokhotov S Yu, Tudorovskiy T Ya 2006 J. Eng. Math. 55 (1–4) 183
• [17] Leble S B and Rohraff D W 2006 Physica Scripta 123 140
• [18] Maslov V P 1965, Izd. MGU, Moscow (in Russian)
• [19] Maslov V P 1976 Operator methods, Mir, Moscow
• [20] Perelomova A A 2009 Archives of Acoustics 34 (2) 127
• [21] Perelomova A and Leble S 2005 TMF 144 1030
• [22] Leble S and Vereshchagina I 2013 The method of dynamic projection operators in the theory of hyperbolic systems of partial differential equations with variable coefficient, 2nd International Conference “High-performance computing and mathematical models and algorithms”, dedicated to Carl Jacobi

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).