Results 1 to 10 of about 130 (127)
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered. The analogue of D'Alembert formula is obtained as a solution that allows describing the propagation of initial displacement, initial ...
J. O. Yakovleva
doaj +4 more sources
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
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
Research on One-to-Two Internal Resonance of Sling and Beam of Suspension Sling–Beam System
Buildings, 2023 An approach is presented to investigate the 1:2 internal resonance of the sling and beam of a suspension sling–beam system. The beam was taken as the geometrically linear Euler beam, and the sling was considered to be geometrically nonlinear. The dynamic
Lixiong Gu +5 more
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
The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 To every Darboux integrable system there is an associated Lie group $G$ which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group $G$.
Anderson, I.M., Fels, M.E.
openaire +4 more sources
The fractional d'Alembert's formulas
Journal of Functional Analysis, 2019 In this paper we develop generalized d'Alembert's formulas for abstract fractional integro-differential equations and fractional differential equations on Banach spaces. Some examples are given to illustrate our abstract results, and the probability interpretation of these fractional d'Alembert's formulas are also given.
Li, Cheng-Gang +3 more
openaire +3 more sources
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
doaj +1 more source