Skip to main content
SpringerLink
Log in

A certain Fredholm partial integro-differential equation of the third order

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We study the unique solvability of the initial value problem for a nonlinear partial Fredholm integro-differential equation of the third order with a degenerate kernel. First, we adapt the degenerate kernel method developed for a partial Fredholm integro-differential equation of the second kind for solving Fredholm integro-differential equations of the third order. After solving the corresponding system of algebraic equations, we obtain a Volterra integral equation of the second kind. Then we apply the method of successive approximations combined with the method of contractive maps.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Algazin, S. D. and Kiiko, I. A. Aeroelastic Vibrations and Stability of Plates and Shells (Nauka, Moscow, 2006) [in Russian].

    Google Scholar 

  2. Shkhanukov, M. Kh. “On Some Boundary Value Problems for an Equation of Third Order Arising From Simulation of Filtration of a Fluid in Porous Media,” Differ. Uravn. 18(4), 689–699 (1982).

    MathSciNet  MATH  Google Scholar 

  3. Andreev, A. A. and Yakovleva, Yu. O. “The Characteristic Problem for a System of General Hyperbolic Differential Equations of the Third Order in a General Form with Nonmultiple Characteristics,” Vestn. SamGTU. Ser. Fiz.-Matem. Nauki 30, No. 1, 31–36 (2013).

    Article  Google Scholar 

  4. Zikirov, O. S. “Dirichlet Problem for Third-Order Hyperbolic Equations,” Russian Mathematics (Iz. VUZ) 58, No. 7, 53–60 (2014).

    MathSciNet  Google Scholar 

  5. Repin, O. A. and Kumykova, S. K. “A Problem with Shift for the Third-Order Equation with Discontinuous Coefficients,” Vestn. SamGTU. Ser. Fiz.-Matem. Nauki 29, No. 4, 17–25 (2012).

    Article  Google Scholar 

  6. Sabitov, K. B. “A Boundary-Value Problem for a Third-Order Equation of Mixed Type,” Dokl. Math. 80, No. 1, 565–568 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. Sabitov, K. B. “Dirichlet Problem for a Third-Order Equation of Mixed Type in a Rectangular Domain,” Differ. Equ. 47, No. 5, 706–714 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  8. Sopuev, A. and Arkabaev, N. K. “Interface Problems for Linear Pseudo-Parabolic Equations of the Third Order,” Vestn. TomGU. Matem. Mekhan. 21, No. 1, 16–23 (2013).

    Google Scholar 

  9. Yuldashev, T. K. “The Inverse Problem for One Nonlinear Integro-Differential Equation of the Third Order,” Vestn. SamGU. Ser. Estestvennonauchnaya, No. 1, 58–66 (2013).

    Google Scholar 

  10. Yuldashev, T. K. “The Inverse Problem for One Partial Integro-Differential Equation of the Third Order,” Vestn. SamGTU. Ser. Fiz.-Matem. Nauki 34, No. 1, 56–65 (2014).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Siberian State Aerospace University, pr. Krasnoyarskii Rabochii 31, Krasnoyarsk, 660014, Russia

    T. K. Yuldashev

Authors
  1. T. K. Yuldashev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. K. Yuldashev.

Additional information

Original Russian Text © T.K. Yuldashev, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 9, pp. 74–79.

Submitted by R.B. Salimov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuldashev, T.K. A certain Fredholm partial integro-differential equation of the third order. Russ Math. 59, 62–66 (2015). https://doi.org/10.3103/S1066369X15090091

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15090091

Keywords

Search

Navigation