Skip to main content
Log in

Fourier transformation method for some types of nonlinear partial differential equations

  • Research Articles
  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We propose a method for analyzing the Cauchy problem for a wide class of equations with power-like nonlinearities. The method is based on the Fourier transformation, which allows reducing the original equation to an integro-differential one. We prove the existence of solutions.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. D. Polyanin, V. Zaitsev, and A. I. Zhurov, Solution Methods for Nonlinear Equations of Mathematical Physics and Mechanics, Fizmatlit, Moscow (2005).

    Google Scholar 

  2. V. I. Gishlarkaev, “A method for representing solutions of the Cauchy problem for linear partial differential equations,” Sb. Math., 209, 222–240 (2018).

    Article  MathSciNet  Google Scholar 

  3. J. D. Murray, Lectures on Nonlinear Differential Equation Models in Biology, Oxford Univ. Press, Oxford (1977).

    MATH  Google Scholar 

  4. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, Fourier Analysis, Self-Adjointness, Academic Press, New York–London (1975).

    MATH  Google Scholar 

  5. L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. I, Distribution Theory and Fourier Analysis (Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 256), Springer, Berlin (1983).

    MATH  Google Scholar 

  6. E. F. Beckenbach and R. Bellman, An Introduction to Inequalities (New Mathematical Library, Vol. 3), Random House, New York (1961).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Gishlarkaev.

Ethics declarations

The author declares no conflicts of interest.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 361-375 https://doi.org/10.4213/tmf10036.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gishlarkaev, V.I. Fourier transformation method for some types of nonlinear partial differential equations. Theor Math Phys 207, 713–726 (2021). https://doi.org/10.1134/S0040577921060039

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577921060039

Keywords

Navigation