# On a diagonal system of the first-order partial differential equations from two independent variables

• T. М. Aldibekov Аl-Farabi Kazakh National University
• M. M. Aldazharova Аl-Farabi Kazakh National University

### Abstract

A diagonal system of three first-order partial differential equations in two indep endent variablesis cons idered. The equations entering into the diagonal system are indep endent from each other,therefore, the compatibility condition of the system do es not arise. We consider the asymptotic b ehavior of solutions at an infinitely distant p oint, with resp ect to some parameter. The main placein the system is o ccup ied by a nonlinear first-order partial differential equation, the remainingequations are adjoining equations, the solutions of which contain the initial value of one indep endent variable as a parameter. The attached equations are chosen appropriately, and the solutionto the system is already studied, w hich already has an internal connection. The adjoint equationsare linear first-orde r partial differential equations. Using the fact that the zero solutions of thecharacteristic equations are asymptotically stable on Lyapunov, the condi tion s when the set ofthree differential equations, c on sidered as a diagonal system of partial differential equations of thefirst order, has a solution w ith certain initial values and is an infinitesimal function in the vicinityof an infini te ly remote p oint are de scrib ed . Metho ds of the theory of functions and differentialinequalities in the theory of first-order differential equations are used.

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Published
2020-04-05
How to Cite
ALDIBEKOV, T. М.; ALDAZHAROVA, M. M.. On a diagonal system of the first-order partial differential equations from two independent variables. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 105, n. 1, p. 3-9, apr. 2020. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/698>. Date accessed: 07 june 2020.
Citation Formats
Section
Mathematics
Keywords differential equations, diagonal system, first order partial derivatives, asymptotic behavior