Characteristic problems with normal derivatives for hyperbolic systems

Abstract

We consider characteristic problems with normal derivatives for a hyperbolic systemwith two independent variables. Using the Riemann method, we obtain solvability conditions for these problems accurate to several arbitrary constants.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    V. I. Zhegalov, “Relation Between the Boundary Values of Goursat Problem and the Normal Derivatives,” in Conditionally Well-Posed Problems (Moscow, TVP Sc. Publ., 1994), pp. 346–349.

    Google Scholar 

  2. 2.

    M. P. Kotukhov, “On Some Differential Properties of Solutions of a Partial Differential Equation,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 5, 59–62 (1996). [RussianMathematics (Iz. VUZ) 40 (5), 57–60 (1996)].

    Google Scholar 

  3. 3.

    A. N. Mironov, “On the Relation Between the Boundary Values of the Goursat Problem with Normal Derivatives of the Third Order,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 10, 23–26 (1999). [RussianMathematics (Iz. VUZ) 43 (10), 21–24 (1999)].

    Google Scholar 

  4. 4.

    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 

  5. 5.

    V. I. Zhegalov and L. B. Mironova, “One System of Equations with Double Major Partial Derivatives,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 3, 12–21 (2007). [Russian Mathematics (Iz. VUZ) 51 (3), 9–18 (2007)].

    Google Scholar 

  6. 6.

    V. I. Zhegalov, “A Problem with Normal Derivatives in Boundary Conditions for a System of Differential Equations,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 8, 70–72 (2008). [Russian Mathematics (Iz. VUZ) 52 (8), 58–60 (2008)].

    Google Scholar 

  7. 7.

    L. B. Mironova, “The Riemann Method inR n for a System withMultiple Characteristics,” Izv. Vyssh.Uchebn. Zaved.Mat., No. 1, 34–39 (2006) [Russian Mathematics (Iz. VUZ) 50 (1), 32–37 (2006)].

    Google Scholar 

  8. 8.

    P. P.Zabreiko,A. I. Koshelev, et. al. Integral Equations (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to E. A. Sozontova.

Additional information

Original Russian Text © E.A. Sozontova, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 10, pp. 43–54.

About this article

Cite this article

Sozontova, E.A. Characteristic problems with normal derivatives for hyperbolic systems. Russ Math. 57, 37–47 (2013). https://doi.org/10.3103/S1066369X13100046

Download citation

Keywords and phrases

  • hyperbolic system
  • characteristic problem with normal derivatives
  • Riemann method