Skip to main content
Log in

Factorization of equations with dominating higher partial derivative

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We present necessary and sufficient conditions for the factorization of equations with dominating partial derivatives and illustrate the possibility of using our results by examples of two forms of equations of the second and third orders.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bondarenko, B.A., Bazisnye sistemy polinomial’nykh i kvazipolinomial’nykh reshenii uravnenii v chastnykh proizvodnykh (Basis Systems of Polynomial and Quasipolynomial Solutions of Partial Differential Equations), Tashkent: Fan, 1987.

    Google Scholar 

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

    Google Scholar 

  3. Colton, D., Pseudoparabolic Equations in One Space Variable, J. Differential Equations, 1972, vol. 12, no. 3, pp. 559–565.

    Article  MATH  MathSciNet  Google Scholar 

  4. Soldatov, A.P. and Shkhanukov, M.Kh., Boundary Value Problems with A. A. Samarskii’s General Nonlocal Condition for Higher-Order Pseudoparabolic Equations, Dokl. Akad. Nauk SSSR, 1987, vol. 297, no. 3, pp. 547–552.

    MathSciNet  Google Scholar 

  5. Utkina, E.A., On a Differential Equation with a Higher Partial Derivative in Three-Dimensional Space, Differ. Uravn., 2005, vol. 41, no. 5, pp. 697–701.

    MathSciNet  Google Scholar 

  6. Utkina, E.A., On the General Case of the Goursat Problem, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 8, pp. 57–62.

    Google Scholar 

  7. Mironov, A.N., The Riemann Method for Equations with the Highest Partial Derivative in R n, Sibirsk. Mat. Zh., 2006, vol. 47, no. 3, pp. 584–594.

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhegalov, V.I. and Koshcheeva, O.A., Order Reduction for a Class of Partial Differential Equations, Dokl. Akad. Nauk, 2006, vol. 406, no. 5, pp. 593–597.

    MathSciNet  Google Scholar 

  9. Zaitsev, V.F. and Polyanin, A.D., Spravochnik po obyknovennym differentsial’nym uravneniyam (A Handbook on Ordinary Differential Equations), Moscow, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Zhegalov.

Additional information

Original Russian Text © V.I. Zhegalov, O.A. Tikhonova, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 1, pp. 66–72.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhegalov, V.I., Tikhonova, O.A. Factorization of equations with dominating higher partial derivative. Diff Equat 50, 66–72 (2014). https://doi.org/10.1134/S0012266114010091

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266114010091

Keywords

Navigation