Skip to main content
SpringerLink
Log in

Unique Solvability of an Initial–Boundary Value Problem for a System of Third-Order Partial Differential Equations

  • SHORT COMMUNICATIONS
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We consider an initial–boundary value problem for a system of third-order partial differential equations in a rectangular domain. By introducing a new unknown function, we reduce the problem to an equivalent one consisting of a nonlocal problem for a system of second-order hyperbolic equations with parameters and integral relations. An iterative algorithm is proposed for approximately solving the equivalent problem, and its convergence is proved. Sufficient conditions in terms of the input data are established for the existence of a unique classical solution of the original problem.

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. Ptashnyck, B.I., Nekorrektnye granichnye zadachi dlya differentsial’nykh uravnenii s chastnymi proizvodnymi (Ill-Posed Boundary Value Problems for Partial Differential Equations), Kiev: Nauk. Dumka, 1984.

    Google Scholar 

  2. Nakhushev, A.M., Uravneniya matematicheskoi biologii (Equations of Mathematical Biology), Moscow: Vyssh. Shkola, 1995.

    MATH  Google Scholar 

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

    Google Scholar 

  4. Nakhushev, A.M., Zadachi so smeshcheniem dlya uravnenii v chastnykh proizvodnykh (Problems with Displacement for Partial Differential Equations), Moscow: Nauka, 2006.

    Google Scholar 

  5. Asanova, A.T. and Dzhumabaev, D.S., Well-posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations, J. Math. Anal. Appl., 2013, vol. 402, no. 1, pp. 167–178.

    Article  MathSciNet  Google Scholar 

  6. Assanova, A.T. and Imanchiev, A.E., On conditions of the solvability of nonlocal multi-point boundary value problems for quasi-linear systems of hyperbolic equations, Eurasian Math. J., 2015, vol. 6, no. 4, pp. 19–28.

    MathSciNet  MATH  Google Scholar 

  7. Asanova, A.T., Multipoint problem for a system of hyperbolic equations with mixed derivative, J. Math. Sci. (US), 2016, vol. 212, no. 3, pp. 213–233.

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan for 2020–2022, project no. AP08955461.

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Almaty, 05010, Kazakhstan

    A. T. Assanova

Authors
  1. A. T. Assanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. T. Assanova.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Assanova, A.T. Unique Solvability of an Initial–Boundary Value Problem for a System of Third-Order Partial Differential Equations. Diff Equat 57, 111–116 (2021). https://doi.org/10.1134/S0012266121010092

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266121010092

Search

Navigation