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Analysis of dissipative structures based on the gauss variational principle

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Abstract

The Gauss variational principle is suggested as a method of finding the solutions of dissipative systems. Using as an example a system of two reaction-diffusion equations, approximate solutions are found for the case of auto-solitons and periodic dissipative structures.

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References

  1. J. Marsden and M. MacCracken, Bifurcation of Cycle Production and Its Applications [Russian translation], Mir, Moscow (1980), 368 pp.

    Google Scholar 

  2. J. Henry, Geometric Theory of Semilinear Parabolic Equations [Russian translation], Mir, Moscow (1985), 376 pp.

    Google Scholar 

  3. A. K. Prikarpatskii and I. V. Mikityuk, Algebraic Elements of the Integrability of Nonlinear Dynamic Systems [in Russian], Nauk. Dumka, Kiev (1991), 375 pp.

    Google Scholar 

  4. V. G. Samoilenko, Quasi-invariant Deformations of Invariant Submanitblds of Hamiltonian Dynamic Systems and Their Ergodicity [in Russian], Preprint 91.56, Institute of Mathematics, Academy of Sciences of Ukraine, Kiev (1991), 25 pp.

    Google Scholar 

  5. B. D. Vujanovic and S. E. Jones, Variational Methods in Nonconservative Phenomena, Academic, London (1989), 370 pp.

    Google Scholar 

  6. G. Nikolis and I. Prigogine, Self-Organization in Nonequilibrium Systems [Russian translation], Mir, Moscow (1979), 512 pp.

    Google Scholar 

  7. H. Haaken, Synergetics [Russian translation], Mir, Moscow (1980), 404 pp.

    Google Scholar 

  8. Yu. M. Romanovskii, N. V. Stepanova, and D. S. Chernavskii, Mathematical Biophysics [in Russian], Nauka, Moscow (1984), 304 pp.

    Google Scholar 

  9. B. S. Kerner and V. V. Osipov, Autosolitons [in Russian], Nauka, Moscow (1991), 180 pp.

    Google Scholar 

  10. V. V. Gafiychuk, B. S. Kerner, V. V. Osipov, and I. I. Lazurchak, “Fluctuating autosolitons in active distributed media,” Mikroélektronika,5, No. 2, 180–183 (1986).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Problems of Mechanics and Mathematics, Academy of Sciences of Ukraine, Lvov

    V. V. Gafiychuk & I. O. Lubashevs'kyy

  2. Russian Open University, Moscow

    V. V. Gafiychuk & I. O. Lubashevs'kyy

Authors
  1. V. V. Gafiychuk
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  2. I. O. Lubashevs'kyy
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Additional information

Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1186–1192, September, 1992.

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Gafiychuk, V.V., Lubashevs'kyy, I.O. Analysis of dissipative structures based on the gauss variational principle. Ukr Math J 44, 1085–1090 (1992). https://doi.org/10.1007/BF01058368

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  • DOI: https://doi.org/10.1007/BF01058368

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