“FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD FOR SOLVING THE CAUCHY PROBLEM ASSOCIATED WITH THEM”

Authors

  • Doniyor G’afurovich Rayimov PhD, Associate Professor, Department of General Technical Sciences, Asia International University

DOI:

https://doi.org/10.55640/

Keywords:

The problem of finding the general solution of a first-order quasilinear partial differential equation is reduced to solving a homogeneous differential equation, and the general solution can be obtained by the method of characteristics. The solution of the Cauchy problem is then found by checking the additional condition of the Cauchy problem along the characteristics and introducing a new variable if necessary

Abstract

In this topic, we study first-order partial differential equations, including their quasilinear and linear forms, as well as homogeneous and non-homogeneous types. We also discuss methods for constructing both particular and general solutions of these equations using their characteristic equations and families of characteristic curves, known as first integrals. Furthermore, we examine how to determine the solution of the Cauchy problem posed for such equations based on the obtained general solution.

Downloads

Download data is not yet available.

References

1.Salokhiddinov, M.S. Equations of Mathematical Physics, Tashkent: “Uzbekistan”, 2002.

2.Mixlin, S.G. Course of Mathematical Physics, Moscow, 1968.

3.Sobolev, S.L. Equations of Mathematical Physics, Nauka, Moscow, 1966.

4.Bitsadze, A.V. Equations of Mathematical Physics, Moscow, 1976.

5.Bitsadze, A.V., Kalinichenko, D.F. Collection of Problems on Equations of Mathematical Physics, Moscow, 1977.

Downloads

Published

2026-04-11

Issue

Vol. 5 No. 4 (2026): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

“FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS AND THE METHOD FOR SOLVING THE CAUCHY PROBLEM ASSOCIATED WITH THEM”. (2026). Journal of Multidisciplinary Sciences and Innovations, 5(4), 771-774. https://doi.org/10.55640/

Similar Articles

1-10 of 2137

You may also start an advanced similarity search for this article.