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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 7, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(2):85-98; doi:10.1093/qjmam/hbl023
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Q. Jl Mech. Appl. Math, Vol. 60. No. 2 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Long-range asymptotics of a step signal propagating in a hereditary viscoelastic medium

Andrzej Hanyga{dagger}

( Department of Geosciences, Princeton University, 321B Guyot HallPrinceton, NJ 08544, USA )

{dagger} On leave from Department of Earth Science, University of Bergen, Allégaten 41, 2007 Bergen, Norway. andrzej.hanyga{at}geo.uib.no

Received 12 June 2006. Revise 30 October 2006.
  Abstract

The shape of the asymptotic long-range solution of the scalar linear viscoelastic signaling problem is found for a large class of creep compliances. If the asymptotic growth of the creep compliance at large times is given by a power law then the long-range asymptotic shape of an initial step pulse is given by a function depending exclusively on the value of the exponent in the power law. Two different cases arise corresponding to unbounded and bounded creep compliances. In the first case the asymptotic solution is the solution of a fractional wave equation with a scale factor. In the second case a different universal signal shape function is obtained.


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