Results 21 to 30 of about 175 (144)

D'ALEMBERT FORMULA AND THE DIRECT OR INVERSE PROBLEMS FOR WAVE EQUATION

Acta Mathematica Scientia, 1990
Summary: A new proof of the D'Alembert formula for Cauchy problems for the wave equation is proposed. Some D'Alembert-type formulas for a Cauchy problem with discontinuous coefficients or a semi-infinite initial boundary value problem are proposed. The characteristic methods for the direct and inverse problems of the stress wave equation for a uniform ...
Ruxun Liu
core   +3 more sources

Movement of a railway car rolling down a classification hump with a tailwind

MATEC Web of Conferences, 2018
The purpose of this paper is to calculate kinematic parameters of a railway car moving with a tailwind for designing a classification hump. The calculation of kinematic parameters is based on the d'Alembert principle, and the physical speed and distance ...
Turanov Khabibulla, Gordienko Andrey
doaj   +2 more sources

Nonlinear d'Alembert formula for discrete pseudospherical surfaces

Nonlinear d'Alembert formula for discrete pseudospherical surfaces
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature (pseudospherical) surfaces in Euclidean three space. We also compute two examples by this formula in detail.
Kobayashi, Shimpei
core   +1 more source

Boundary-value problems for wave equations with data on the whole boundary [PDF]

Electronic Journal of Differential Equations, 2016
In this article we propose a new formulation of boundary-value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary.
Makhmud A. Sadybekov, Nurgissa A. Yessirkegenov   +1 more
doaj   +1 more source

Boundary control problem for a hyperbolic equation loaded along one of its characteristics [PDF]

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This paper investigates the unique solvability of the boundary control problem for a one-dimensional wave equation loaded along one of its characteristic curves in terms of a regular solution.
A.Kh. Attaev
doaj   +2 more sources

On The Solutions of Wave Equation in Three Dimensions using D'alembert Formula

International Journal of Mathematics Trends and Technology, 2017
null null, Mustafa A Sabri, Maan A Rasheed   +2 more
core   +2 more sources

Weakly non-linear extension of d'Alembert's formula [PDF]

IMA Journal of Applied Mathematics, 2012
We consider a weakly nonlinear solution of the Cauchy problem for the regularised Boussinesq equation, which constitutes an extension of the classical d'Alembert's formula for the linear wave equation. The solution is given by a simple and explicit formula, expressed in terms of two special functions solving the initial-value problems for two Korteweg ...
Khusnutdinova, K. R., Moore, K. R.
openaire   +2 more sources

A generalization of d’Alembert formula [PDF]

Proceedings Mathematical Sciences, 2007
In this paper we find a closed form of the solution for the factored inhomogeneous linear equation \begin{equation*} \prod_{j=1}^{n}(\frac{\hbox{d}}{\hbox{d}t}-A_{j}) u(t) =f(t). \end{equation*} Under the hypothesis $A_{1},A_{2}, ..., A_{n}$ are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on
Chang, Yu-Hsien, Hong, Cheng-Hong
openaire   +3 more sources

Fórmulas de Poisson e de Kirchhoff deduzidas por volumes de controle

REMAT, 2022
Este artigo apresenta uma dedução alternativa para as fórmulas de Poisson e de Kirchhoff, que resolvem o problema de valor inicial governado pela equação da onda em duas e três dimensões, respectivamente.
Adriano Rodrigues de Melo
doaj   +1 more source

On Classic Solution of the Problem for a Homogeneous Wave Equation with Fixed End-Points and Zero Initial Velocity [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2019
The paper gives necessary and sufficient conditions of classic solution for a homogeneous wave equation with a summable potential, fixed end-point, and zero initial velocity.
Avgust Petrovich Khromov
doaj   +1 more source