Results 21 to 30 of about 180 (151)

One characteristic problem for the general hyperbolic differential equation of the third order with nonmultiple characteristics

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012
In the paper we consider the well-posed characteristic problem for the general hyperbolic differential equation of the third order with nonmultiple characteristics. The solution of this problem is constructed in an explicit form. The illustrative example
J. O. Yakovleva
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Initial Value Problems for System of Wave Equations

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2009
We present solutions to the Cauchy problem and the Goursat problem for system of wave equations. Discharged analogue d'Alembert formula for system of wave equations.
S. V. Leksina
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BOUNDARY VALUE PROBLEM FOR A GENERALIZED TELEGRAPH EQUATION OF FRACTIONAL ORDER WITH VARIABLE COEFFICIENTS

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2016
In this paper, we construct the solution to the Goursat problem for a generalized telegraph equation of fractional order with variable coefficients.
Pshibikhova R. A.
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On problems with displacement in boundary conditions for hyperbolic equation

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are
Elena A Utkina
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On the Representation of the Goursat Boundary Problem Solution for the First Order Partial Derivatives Stochastic Hyperbolic Equations

Известия Иркутского государственного университета: Серия "Математика", 2023
We study the standard canonical form of a stochastic analog of a system of linear partial differential equations of first order hyperbolic type with Goursat boundary conditions.
K.B. Mansimov, R.O. Mastaliyev
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Goursat problem in Hyperbolic partial differential equations with variable coefficients solved by Taylor collocation method [PDF]

Iranian Journal of Numerical Analysis and Optimization
The hyperbolic partial differential equation (PDE) has important practical uses in science and engineering. This article provides an estimate for solving the Goursat problem in hyperbolic linear PDEs with variable coefficients.
F. Birem, A. Boulmerka, H. Laib, C. Hennous   +3 more
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Goursat’s problem on the plane for a quasilinear hyperbolic equation

Doklady of the National Academy of Sciences of Belarus, 2022
A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator.
Korzyuk, Viktor Ivanovich, Kovnatskaya, Ol'ga Anatol'evna, Sevastyuk, Vladimir Aleksandrovich   +2 more
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Existence and uniqueness of nonlinear Goursat problem in the class of Denjoy–Carleman

Partial Differential Equations in Applied Mathematics
The problem of existence and uniqueness of nonlinear Goursat is studied by Claude Wagschal in different spaces: holomorphic spaces, partially holomorphic, continuous-Gevrey and Gevrey-holomorphic.
Smail Latreche, Kaddour Guerbati, Rafik Guefaifia, Ibrahim Mekawy, Asma Alharbi, Rashid Jan   +5 more
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A uniqueness theorem for a goursat-type problem

Applied Mathematics Letters, 1992
Consider the problem (1) \(u_{tt}- \Delta u+ q(x)u=0\), \(x\in\mathbb{R}^ 3\), \(-r\leq t\leq r\), \(r=| x|\), (2) \(u=0\) at \(t=\pm r\), \[ \varliminf_{R\to\infty} \int_{| s|=R} \int_{-R}^ R | u_ r\mp u_ t|^ 2 dt ds=0.\tag{3} \] The boundary data are given on the characteristic cone \(t=\pm r\). Condition (3) is a condition at infinity. Assume that \(
Mishnaevskii, P.A., Ramm, A.G.
openaire   +2 more sources

ON MATHEMATICAL MODELS OF THE ALLER EQUATION

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2016
The solution to the Goursat problem is written out explicitly for a hyperbolic secondorder loaded equation, proposed as a mathematical model of Aller equation under certain conditions.
Khubiev K. U.
doaj   +1 more source