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Determination of an unknown curve of discontinuity of the solution of a mixed problem for a quasilinear hyperbolic system

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Literature cited

  1. R. Courant and K. Friedrichs, Supersonic Flow and Shock Waves, Wiley-Interscience, New York (1948).

    Google Scholar 

  2. A. S. Vol'mir, Shells in Fluid and Gas Flow: Problems of Aeroelasticity [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  3. A. S. Vol'mir, Shells in Fluid and Gas Flow: Problems of Hydroelasticity [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. C. Denson Hill, “A hyperbolic free boundary problem,” J. Math. Anal. Appl.,31, No. 1, 117–129 (1971).

    Google Scholar 

  5. T. E. Mel'nik, “A Stefan type problem for a first-order hyperbolic system,” Ukr. Mat. Zh.,34, No. 3, 380–384 (1982).

    Google Scholar 

  6. Z. O. Mel'nik, “A problem with unknown boundaries for a first-order hyperbolic system,” in: Partial Differential Equations and Free Boundary Problems [in Russian], Naukova Dumka, Kiev (1983), pp. 77–79.

    Google Scholar 

  7. Z. O. Mel'nik, “A mixed problem with an unknown boundary for a general two-dimensional second-order hyperbolic equation,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 8, 13–15 (1983).

    Google Scholar 

  8. T. E. Mel'nik, “A two-phase Stefan type problem for a general two-dimensional secondorder hyperbolic equation,” in: Partial Differential Equations and Free Boundary Problems [in Russian], Naukova Dumka, Kiev (1983), pp. 79–82.

    Google Scholar 

  9. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  10. P. Hartman, Ordinary Differential Equations, Wiley, New York (1964).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 4, pp. 443–450, July–August, 1985.

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Kazakov, K.Y., Morozov, S.F. Determination of an unknown curve of discontinuity of the solution of a mixed problem for a quasilinear hyperbolic system. Ukr Math J 37, 352–357 (1985). https://doi.org/10.1007/BF01055947

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  • DOI: https://doi.org/10.1007/BF01055947

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