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Nonlinear stage of instability evolution in a monostable active medium

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Abstract

A theoretical analysis is made of the nonlinear stage of instability evolution in a monostable active medium described by a “reaction-diffusion” type equation. The boundary of that region of the medium in which instability develops propagates at constant velocity. Group-theoretical analysis of the problem yields an analytic expression for the propagation velocity of this boundary. The results may be important for the analysis of instability evolution in a wide range of active media.

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References

  1. V. A. Vasil’v, Yu. M. Romanovskii, and V. G. Yakhno, Autowave Processes [in Russian], Nauka, Moscow (1987), 240 pp.

    Google Scholar 

  2. A. Yu. Loskutov and A. S. Mikhailov, Foundations of Synergetics, 2nd ed., Springer, New York (1994–1996) [Russ. orig., Nauka, Moscow (1990), 272 pp.].

    Google Scholar 

  3. A. Vl. Gurevich and R. G. Mints, Usp. Fiz. Nauk 142(1), 61 (1984) [Sov. Phys. Usp. 27, 19 (1984)].

    MathSciNet  Google Scholar 

  4. Yu. M. L’vovskii, Pis’ma Zh. Tekh. Fiz. 15(15), 39 (1989) [Sov. Tech. Phys. Lett. 15, 596 (1989)].

    Google Scholar 

  5. S. V. Petrovskii, Zh. Tekh. Fiz. 64(8), 1 (1994) [Tech. Phys. 39, 747 (1994)].

    Google Scholar 

  6. A. A. Pukhov, Supercond. Sci. Technol. 10, 547 (1997).

    ADS  Google Scholar 

  7. N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics (Reidel, Dordrecht, 1985) [Russ. original, Nauka, Moscow, 1983, 280 pp.].

    Google Scholar 

  8. G. W. Bluman and S. Kumei, Symmetries and Differential Equations (Springer-Verlag, New York, 1989).

    Google Scholar 

  9. L. Dresner, Similarity Solutions of Nonlinear Partial Differential Equations (Pitman, London, 1983).

    Google Scholar 

  10. L. Dresner, IEEE Trans. Magn. 21, 392 (1985).

    Article  Google Scholar 

  11. A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhalov, Blow-up in Quasilinear Parabolic Equations, W. de Gruyter, New York (1995) [Russ. orig., Nauka, Moscow (1987), 477 pp.].

    Google Scholar 

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Authors and Affiliations

  1. Joint Institute of High Temperatures, Scientific-Research Center of Applied Problems in Electrodynamics, Russian Academy of Sciences, Moscow

    A. A. Pukhov

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  1. A. A. Pukhov
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Pis’ma Zh. Tekh. Fiz. 24, 10–15 (July 26, 1998)

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Pukhov, A.A. Nonlinear stage of instability evolution in a monostable active medium. Tech. Phys. Lett. 24, 545–546 (1998). https://doi.org/10.1134/1.1262187

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  • DOI: https://doi.org/10.1134/1.1262187

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