The D'Alembert Type Solution of the Cauchy Problem for the Homogeneous with Respect to Fourth Order Derivatives for Hyperbolic Equation
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Springer International Publishing Ag
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
In this paper the D'Alembert type solution for the following Sigma(i=0) a(i) partial derivative(4)u (x, t)/partial derivative t(4)-(i)partial derivative x(i) = 0, partial derivative(k) u(x, t)/partial derivative t(k) |(t=0) = phi(k) (x), (k = 0, 1, 2, 3) Cauchy problem is constructed. Here, a(i), (i = 1, 2, 3, 4) and fk (x), (k = 1, 2, 3, 4) are given constants and functions, respectively. The cases where the roots of the characteristic equation are folded are examined and compact expressions for the solutions are obtained. The obtained solutions allow proving the uniqueness and existence of the solutions of the considered problem.
Description
17th International Conference on Computational Science and its Applications (ICCSA) -- JUL 03-06, 2017 -- Trieste, ITALY
Keywords
D'Alembert type solution, Fourth order hyperbolic equation
Journal or Series
Computational Science And Its Applications - Iccsa 2017, Pt Vi
WoS Q Value
N/A
Scopus Q Value
Q3
Volume
10409
