Differential and Integral Equations

Asymptotic analysis of the abstract telegraph equation

Ted Clarke, Eugene C. Eckstein, and Jerome A. Goldstein

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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).

Article information

Source
Differential Integral Equations, Volume 21, Number 5-6 (2008), 433-442.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038626

Mathematical Reviews number (MathSciNet)
MR2483262

Zentralblatt MATH identifier
1224.35293

Subjects
Primary: 35L90: Abstract hyperbolic equations
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35B40: Asymptotic behavior of solutions 35K90: Abstract parabolic equations 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations

Citation

Clarke, Ted; Eckstein, Eugene C.; Goldstein, Jerome A. Asymptotic analysis of the abstract telegraph equation. Differential Integral Equations 21 (2008), no. 5-6, 433--442. https://projecteuclid.org/euclid.die/1356038626


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