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2008 Asymptotic analysis of the abstract telegraph equation
Ted Clarke, Eugene C. Eckstein, Jerome A. Goldstein
Differential Integral Equations 21(5-6): 433-442 (2008).

Abstract

It is known that each solution of the telegraph equation \begin{equation} u^{\prime \prime}(t)+2au^{\prime}(t)+A^2u(t)=0, \tag*{(0.1)} \end{equation} $(A=A^* $on$\: \mathcal {H}, a>0)$ is approximately equal to some solution of the abstract heat equation, \begin{equation} 2av^\prime(t) + A^2v(t)=0. \tag*{(0.2)} \end{equation} It is shown how to find $v(0)$, in terms of $u(0)$ and $u^\prime(0)$, so that one can say that a given solution of (0.1) is like a specific solution of (0.2).

Citation

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Ted Clarke. Eugene C. Eckstein. Jerome A. Goldstein. "Asymptotic analysis of the abstract telegraph equation." Differential Integral Equations 21 (5-6) 433 - 442, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35293
MathSciNet: MR2483262

Subjects:
Primary: 35L90
Secondary: 34G10, 35B40, 35K90, 47D06, 47N20

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 5-6 • 2008
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