Application of the riemann method to a factorized equation in an n-dimensional space

Abstract

We obtain sufficient conditions for the unique solvability of the characteristic boundary problem for one hyperbolic equation.

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References

  1. 1.

    S. E. Elubaev, “A Boundary-Value Problem for a Hyperbolic Equation,” Sib. Matem. Zhurn. 2(4), 510–519 (1961).

    MathSciNet  MATH  Google Scholar 

  2. 2.

    S. E. Elubaev, “A Boundary-Value Problem for a Hyperbolic Equation of the Third Order with Two Independent Variables,” Vestn. Akad. Nauk Kazakhsk. SSR, No. 6, 54–62 (1962).

  3. 3.

    T. D. Dzhuraev, “On Equations of Mixed-Composite Type,” Izv. Akad. Nauk Uzb. SSR. Ser. Fiz.-Matem., No. 6, 3–14 (1961).

  4. 4.

    T. D. Dzhuraev, “On Boundary-Value Problems for Equations of Mixed-Composite Type,” Sib. Matem. Zhurn., 4(4), 775–787 (1963).

    MATH  Google Scholar 

  5. 5.

    Ni Xingtang, “Boundary-Value Problem with Three Characteristic Supports for Linear Totally Hyperbolic Equation of the Third Order,” Kexue Tongbao 25(5), 361–369 (1980).

    MathSciNet  MATH  Google Scholar 

  6. 6.

    T. D. Dzhuraev and Ya. Popelek, “On the Canonical Forms of Third-Order Partial Differential Equations,” Usp. Mat. Nauk 44(4), 237–238 (1989).

    MathSciNet  Google Scholar 

  7. 7.

    V. I. Zhegalov, “On One Boundary Problem for a Third Order Partial Differential Equation,” in Proc. of Intern. Sci. Conf. ’spectral Theory of Differential Operators and Related Problems’, Sterlitamak, June 24–26, 2003 (Gilem, Ufa, 2003), pp. 119–123.

  8. 8.

    V. I. Zhegalov and A. N. Mironov, “A Remark on Spatial Boundary-Value Problems for Hyperbolic Equations,” Differents. Uravn. 46(3), 364–371 (2010).

    MathSciNet  Google Scholar 

  9. 9.

    V. I. Zhegalov and A. N. Mironov, Differential Equations with Major Partial Derivatives (Kazansk. Matem. Ob-vo, Kazan, 2001) [in Russian].

    Google Scholar 

  10. 10.

    A. N. Mironov, “On the Riemann Method for Solving One Mixed Problem,” Vestn. Samarsk. Tekhn. Univ. Ser. Fiz.-Matem. Nauk, No. 2, 27–32 (2007).

  11. 11.

    A. N. Mironov, “The Riemann Method for Equations with Leading Partial Derivative in R n,” Sib. Matem. Zhurn. 47(30), 584–594 (2006).

    MathSciNet  MATH  Google Scholar 

  12. 12.

    V. I. Zhegalov and A. N. Mironov, “Three-Dimensional Characteristic Problems with Normal Derivatives in Boundary Conditions,” Differents. Uravn. 36(6), 833–836 (2000).

    MathSciNet  Google Scholar 

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Correspondence to A. N. Mironov.

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Original Russian Text © A.N. Mironov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 1, pp. 54–60.

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Mironov, A.N. Application of the riemann method to a factorized equation in an n-dimensional space. Russ Math. 56, 48–54 (2012). https://doi.org/10.3103/S1066369X12010070

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Keywords and phrases

  • Riemann method
  • hyperbolic equation