Modeling of the signal propagation in real systems with finite interval and absorption

1Kryvonos, Yu.G
2Selezov, IT
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
2Institute of Hydromechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 4:35-40
Section: Information Science and Cybernetics
Language: Russian

The wave propagation is investigated on the basis of a generalized hyperbolic equation with dissipation describing the wave propagation with finite velocity. The propagation of harmonic waves and the initial boundary-value problem of a propagation of the pulse from the input on a finite interval with full absorption are analyzed on the basis of the Laplace transformation and a numerical inverse transformation.

Keywords: absorption, finite interval, Laplace transform, wave propagation
  1. Wiener N. Cybernetics or control and communication in the animal and the machine, Cambrifge: Massachus. Institute of Techonogy, 1961.
  2. Selezov I. T., Kryvonos Yu. G. Wave problems of biohydrodynamics and biophysics, Kyiv: Nauk. Dumka, 2013 (in Russian).
  3. Mc Cartin B. J. Appl. Math. Sci., 2009, 3, No 42: 2055–2083.
  4. Vabishchevich P. N. BIT Number Math., 2013. DOI 10.1007/s10 543–013–0423–7.
  5. Doetsch G. Anleitung zum praktischen gebrauch der Laplace-Transformation, und der Z-transformation, München: R. Oldenbourg, 1956.
  6. Courant R., Hilbert D. Methods of mathematical physics. V. 2. New York-London: Interscience, 1962.
  7. Kryvonos Yu. G., Selezov I. T. Dopov. Nac. akad. nauk Ukr., 2014, No 9: 40–43 (in Russian).
  8. Maxwell J. C. A dynamical theory of the electromagnetic field, Phil. Trans. Roy. Soc.,1865, 155: 459–512.
  9. Maxwell J. C. Philos. Trans. Roy. Soc., London,1867, 157: 49–88.
  10. Cattaneo C. Atti Seminario Mat. Fis. Univ. Modena, 1948, 3: 83–124.
  11. Vernotte P. C. R. Hebd. Séanc. Acad. Sci., 1958, 246, No 22: 3154–3155; La veritable equation de la chaleur, 1958, 247: No 23: 2103–2105.
  12. Landau L. D., Lifshitz E. M. The Classical Theory of Fields of a Course of Theoretical Physics. V. 2: Pergamon Press, 1971.
  13. Luikov A. V. Int. J. Heat Mass Transfer., 1966, 9: 139–152.
  14. Selezov I. T. Cybernetics and Computat. Eng. Kiev: Nauk. Dumka, 1969, Iss. 1: 31–137 (in Russian).
  15. Selezov I. T., Krivonos Yu. G. Mathematical methods in problems of propagation and diffraction of waves, Kyiv: Nauk. Dumka, 2012 (in Russian).