Classical and generalized invariant solutions of the relaxing hydrodynamics equations

• Autorzy: Vladimirov V.
• Języki publikacji: EN

Abstrakty

EN

We analyze the set of invariant travelling wave solutions of the relaxing hydrodynamics models and state the conditions that guarantee the existence of periodic solutions and limiting to them soliton-like regimes. We also study the existence of the shock wave invariant solutions. In some special case the periodic invariant solution is shown to give rise to the blow-up regime.

Słowa kluczowe

EN

nonlocal models; symmetry; self-similar reduction; qualitative analysis; limit cycle; shock wave solutions; blow-up regimes

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2003
• Tom: Vol. 23
• Strony: 81--94
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr.

Twórcy

autor

Vladimirov V.

• AGH University of Science and Technology, Cracow,

Bibliografia

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• [4] Guckenheimer J., Holmes P.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York, Springer-Verlag 1987
• [5] Danevich T.B., Danylenko V.A., Korolevich V.Yu., Sorokina V.V., Vladimirov V. A.: The Equations of Hydrodynamics for active media. Symmetries, qu alitative analysis and wave structures' evolution. Kiev, 1992 - 82 p. (Preprint / Academy of Sci. of Ukraine. Subbotin Inst. of Geophysics; 92-16)
• [6] Landau L.D., Lifshitz E.M.: Hydrodynamics. Moscow, Nauka Publ. 1984
• [7] Richtmayer R.: Principles of Advanced Mathematical Physics. Vol. 1. New York, Springer-Verlag 1978
• [8] Andronov A.A., Leontovic E. A., Gordon I.I. et al: Dynamic Systems on a Plane. Israel Program of Scientific Translations, Jerusalem, 1973