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1997 Similarity solutions for a class of hyperbolic integrodifferential equations
Hans Engler
Differential Integral Equations 10(5): 815-840 (1997).

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.

Citation

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Hans Engler. "Similarity solutions for a class of hyperbolic integrodifferential equations." Differential Integral Equations 10 (5) 815 - 840, 1997.

Information

Published: 1997
First available in Project Euclid: 1 May 2013

zbMATH: 0892.45005
MathSciNet: MR1741754

Subjects:
Primary: 45K05
Secondary: 35L99, 45D05

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 5 • 1997
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