## Differential and Integral Equations

### Asymptotic analysis of the abstract telegraph equation

#### Abstract

It is known that each solution of the telegraph equation $$u^{\prime \prime}(t)+2au^{\prime}(t)+A^2u(t)=0, \tag*{(0.1)}$$ $(A=A^*$on$\: \mathcal {H}, a>0)$ is approximately equal to some solution of the abstract heat equation, $$2av^\prime(t) + A^2v(t)=0. \tag*{(0.2)}$$ 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