A remark on spatial boundary value problems for hyperbolic equations


We derive sufficient conditions for the unique solvability of two boundary value problems for factorized hyperbolic equations.

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  1. 1.

    Elubaev, S.E., A Boundary Value Problem for a Hyperbolic Equation, Sibirsk. Mat. Zh., 1961, vol. 2, no. 4, pp. 510–519.

    MATH  MathSciNet  Google Scholar 

  2. 2.

    Elubaev, S.E., A Boundary Value Problem for a Hyperbolic Equation of the Third Order with Two Independent Variables, Vestn. Akad. Nauk KazSSR, 1962, no. 6, pp. 54–62.

  3. 3.

    Dzhuraev, T.D., On Equations of Mixed-Composite Type, Izv. Akad. Nauk UzSSR. Ser. Fiz.-Mat. Nauk, 1961, no. 6, pp. 3–14.

  4. 4.

    Dzhuraev, T.D., On Some Boundary Value Problems for Equations of the Mixed-Composite Type, Sibirsk. Mat. Zh., 1963, vol. 4, no. 4, pp. 775–787.

    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, 1980, vol. 25, no. 5, pp. 361–369.

    MATH  MathSciNet  Google Scholar 

  6. 6.

    Zhegalov, V.I., On a Boundary Value Problem for a Third-Order Partial Differential Equation, in Spektral’naya teoriya differentsial’nykh operatorov i rodstvennye problemy: Tr. mezhdunar. nauchn. konf. (Spectral Theory of Differential Operators and Related Problems: Proc. Int. Sci. Conf.), Sterlitamak, 2003, vol. 1, pp. 119–123.

    Google Scholar 

  7. 7.

    Dzhuraev, T.D. and Popelek, Ya., Canonical Forms of Third-Order Partial Differential Equations, Uspekhi Mat. Nauk, 1989, vol. 44, no. 4, pp. 237–238.

    MathSciNet  Google Scholar 

  8. 8.

    Zhegalov, V.I. and Mironov, A.N., Differentsial’nye uravneniya so starshimi chastnymi proizvodnymi (Differential Equations with Leading Partial Derivatives), Kazan, 2001.

  9. 9.

    Zhegalov, V.I., On the Three-Dimensional Riemann Function, Sibirsk. Mat. Zh., 1997, vol. 38, no. 5, pp. 1074–1079.

    MathSciNet  Google Scholar 

  10. 10.

    Zhegalov, V.I. and Mironov, A.N., Three-Dimensional Characteristic Problems with Normal Derivatives in the Boundary Conditions, Differ. Uravn., 2000, vol. 36, no. 6, pp. 833–836.

    MathSciNet  Google Scholar 

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Correspondence to V. I. Zhegalov.

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Original Russian Text © V.I. Zhegalov, A.N. Mironov, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 3, pp. 364–371.

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Zhegalov, V.I., Mironov, A.N. A remark on spatial boundary value problems for hyperbolic equations. Diff Equat 46, 367–374 (2010). https://doi.org/10.1134/S0012266110030067

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  • Integral Equation
  • Arbitrary Function
  • Canonical Form
  • Hyperbolic Equation
  • Auxiliary Variable