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General remarks on dynamic projection method

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Języki publikacji
EN
Abstrakty
EN
A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.
Rocznik
Strony
113--130
Opis fizyczny
Bibliogr. 49 poz.
Twórcy
autor
  • Department of Physics Immanuel Kant Baltic Federal University Al. Nevsky 14, Kaliningrad, Russia
Bibliografia
  • [1] Fock V A 1936 UFN 16 (8) 1070
  • [2] Kovasznay L S G 1953 J. Aero. Sci. 20 657; Chu B-T, Kovasznay L S G 1958 J. Fluid Mech. 3 494
  • [3] Novikov A A 1976 Radiophysics and Quantum Electronics 19 225
  • [4] Novikov A A 1981 Waves and diffraction 2 66
  • [5] Fleck J A Jr. 1970 Phys. Rev. B 1 84
  • [6] Vereshchagina I 1980 Interaction of modes in multidimensional medium with dispersion, M. Sc. Thesis, Kaliningrad State University (Im. Kant Federal University from 2010)
  • [7] Bessarab F, Karpov I and Leble S 2008 Projection operators for the planetary Poincare and Rossby waves in the atmosphere, Vestnik BFU im. Kanta
  • [8] Bessarab F, Kshevetskij S and Leble S 1987 On the Acoustic-Gravity waves Interaction in Atmosphere. Problems of Nonlinear Acoustics, in: Proceedings of IUPAP, IUTAM symposium on Nonlinear Acoustics Ed. Kedrinskii V K, AN USSR, Siberian Division
  • [9] Leble S B and Zaitsev A A 1987 Novye Methody v Teorii Nelinejnych Voln, Kaliningradskij Universitet [Kaliningrad University Press] [New Methods in Nonlinear Waves Theory] (in Russian)
  • [10] Leble S B 1988 Waiveguide Propagation of Nonlinear Waves in Stratified Media, Leningrad University Press (in Russian); 1990 extended ed. in Springer-Verlag
  • [11] Perelomova A 1993 Izv. RAN, Physics of Atm. Ocean 29 (1) 47
  • [12] Perelomova A A 2000 Applied Mathematics Letters 13 93
  • [13] Perelomova A A 2010 Canadian Journal of Physics 88 (4) 293
  • [14] Perelomova A A 2000 Archives of Acoustics 25 451
  • [15] Brezhnev Yu V, Leble S B and Perelomova A A 1993 Physical Express 41 29
  • [16] Perelomova A 2006 Physics Letters A 357 42
  • [17] Perelomova A 2009 Archives of Acoustics 34 (2) 127
  • [18] Perelomova A 2009 Ultrasonics 49 583
  • [19] Perelomova A 2010 Acta Acustica united with Acustica 96 43
  • [20] Perelomova A and Pelc-Garska W 2010 Central European Journal of Physics 8 (6) 855
  • [21] Perelomova A and Wojda P 2011 Central European Journal of Physics 9 (3) 740
  • [22] Perelomova A and Wojda P 2012 Central European Journal of Physics 10 (5) 1116
  • [23] Perelomova A 2013 Acta Physica Polonica A 123 (4) 681
  • [24] Perelomova A 2013 Acta Acustica united with Acustica 99 352
  • [25] Perelomova A A 1998 Acta Acustica 84 (6) 1002
  • [26] Pitois S, Millot G and Wabnitz S 2001 J. Opt. Soc. Am. B 18 (4)
  • [27] Belov V V, Dobrohotov S Yu and Tudorovskiy T Ya 2006 Journal of Engineering Mathematics 55 (1–4) 183
  • [28] Br¨uning J, Grushin V V and Dobrokhotov S Yu 2012 Mathematical Notes 92 (1) 151
  • [29] Br¨uning J, Grushin V V, Dobrokhotov S Yu and Tudorovskii T Ya 2011 Theoretical and Mathematical Physics 167 547
  • [30] Leble S 1988 Nonlinear Waves in Boundary Layer and Turbulence, in: Theses of XX conference Kaliningrad State University 185
  • [31] Leble S B, Popov I Yu and Gugel’ Yu V 1993 Gidromekh. 67 3 (in russian)
  • [32] Perelomova A and Leble S 2002 Tollmien-Shlichting and Sound Waves Interaction: Nonlinear Resonances, in Nonlinear Acoustics at the Beginning of the 21st Century ed. Rudenko O V et al. (MSU) 1 203
  • [33] Perelomova A and Leble S 2005 TMF 144 1030
  • [34] Lebedkina N, Karpov I and Leble S 2012 A method to construct the projection operators for the Poincare and Rossby waves in the atmosphere, Vestnik BFU im. Kanta, vyp. 4, Ser. Fiz.-mat. nauki 21
  • [35] Kinsler P, Radnor S B P and New G H C 2005 Phys. Rev. A 72, 063807
  • [36] Kinsler P 2007 J. Opt. Soc. Am. B 24 2363
  • [37] Kinsler P 2010 Phys. Rev. A 81, 013819
  • [38] Kinsler P 2010 Phys. Rev. A 81, 023808
  • [39] Kuszner M and Leble S 2011 J. Phys. Soc. Jpn. 80, 024002
  • [40] Kuszner M and Leble S 2014 J. Phys. Soc. Jpn. 83, 034005
  • [41] Caloz Ch Metamaterial-Based Electromaagnetic Space, Time and Spacetime Dispersion Engineering, IEEE, Advanced technology for Humanity
  • [42] Ampilogov D and Leble S 2015 arXiv:1512.01682v1 (see also this paper)
  • [43] Ampilogov D and Leble S 2016 Physics Letters A 380 2271
  • [44] Kuszner M, Leble S, Kuszner M, Leble S and Reichel B 2011 Theoretical and Mathematical Physics 168 (1) 977
  • [45] Kuszner M and Leble S 2015 Waveguide Electromagnetic Pulse Dynamics: Projecting Operators Method, in: Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications ed. Porsezian K., Ganapathy R, CRC Press Reference
  • [46] Pedlosky J 1992 Geophysical Fluid Dynamics, Springer
  • [47] Romanov V G and Moshkalev P 2011 Sib. Zh. Industrie. Mat. 14 (3) 87 (in russian)
  • [48] Leble S and Vereshchagina I The method of dynamic projection operators in the theory of hyperbolic systems of partial differential equations with variable coefficients, arXiv:1403.7751
  • [49] Lavrent’ev M M, Reznitskiy K G and Yakhno V G 1986 American Mathematical Society Translations, series 2 130
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dd138b05-83df-4d80-ab60-0ebfdd89c0b1
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