On exact solution of a hyperbolic system of differential equations
- 1 January 2022
- journal article
- Published by Tambov State University - G.R. Derzhavin in Russian Universities Reports. Mathematics
Abstract
The paper considers a hyperbolic system of two first-order partial differential equations with constant coefficients, one of which is nonlinear and contains the square of one of the unknown functions. Moreover, each equation contains two unknown functions which in turn depend on two variables. Exact solutions are found for this system: a traveling wave solution and a self-similar solution. There is also defined the type of initial-boundary conditions which allow to use the constructed general solutions in order to write out a solution of the initial-boundary value problem for the system of differential equations under consideration.Keywords
This publication has 13 references indexed in Scilit:
- An Optimal Control Problem by a Hyperbolic System with Boundary DelayThe Bulletin of Irkutsk State University. Series Mathematics, 2021
- THE SOLUTION OF CAUCHY PROBLEM FOR THE HYPERBOLIC DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER BY THE RIMAN METHODVestnik of Samara University. Natural Science Series, 2019
- Traveling-Wave Solutions of the Kolmogorov–Petrovskii–Piskunov EquationComputational Mathematics and Mathematical Physics, 2018
- Автомодельные решения уравнения типа Бюргерса с квадратично-кубичной нелинейностьюДоклады Академии наук, 2016
- SELF-SIMILAR SOLUTIONS OF GRAVITATIONAL FLOWS DYNAMICS IN INCLINED CHANNELSПРИКАСПИЙСКИЙ ЖУРНАЛ: УПРАВЛЕНИЕ И ВЫСОКИЕ ТЕХНОЛОГИИ, 2016
- Self-Similar Solution of the Problem of a Turbulent Flow in a Round Submerged JetПрикладная механика и техническая физика, 2015
- Self-similar solution of the plane problem of the evolution of a hydraulic fracture crack in an elastic mediumJournal of Applied Mathematics and Mechanics, 2010
- A solution to the hydraulic fracture problem in the traveling wave formMoscow University Mechanics Bulletin, 2009
- Finite-difference schemes for solving multidimensional hyperbolic equations and their systemsComputational Mathematics and Mathematical Physics, 2007
- Об автомодельном решении одного уравнения третьего порядка с кратными характеристикамиJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2007