## Differential and Integral Equations

### Similarity solutions for a class of hyperbolic integrodifferential equations

Hans Engler

#### Abstract

For a class of hyperbolic partial integrodifferential equations of the form $u_{tt} - u_{xx} + a*u_{xx} = 0$, fundamental solutions are found that depend on the similarity variable $\xi =x(t-|x|)^{-\alpha}$, where $\alpha \in (0,1)$ and the integral kernel $a$ behaves like $t^{-\alpha}$ near $t=0$. The asymptotic behavior of these solutions in various scaling limits and their regularity is discussed. Applications to solutions of general initial-value problems of such equations are given.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 5 (1997), 815-840.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367438621

Mathematical Reviews number (MathSciNet)
MR1741754

Zentralblatt MATH identifier
0892.45005

#### Citation

Engler, Hans. Similarity solutions for a class of hyperbolic integrodifferential equations. Differential Integral Equations 10 (1997), no. 5, 815--840. https://projecteuclid.org/euclid.die/1367438621