Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Kolsky (1956)
LXXI. The propagation of stress pulses in viscoelastic solidsPhilosophical Magazine, 1
(2005)
Physically acceptable viscoelastic models
I. Sokolov, A. Chechkin, J. Klafter (2004)
Distributed-Order Fractional KineticsarXiv: Statistical Mechanics
(1975)
Viscoélasticité linéaire and functions complètement monotones
A. Pipkin (1988)
Asymptotic behaviour of viscoelastic wavesQuarterly Journal of Mechanics and Applied Mathematics, 41
M. Vuilleumier (1976)
Slowly varying functions in the complex planeTransactions of the American Mathematical Society, 218
W. Kuhn, O. Künzle, A. Preissmann (1947)
Relaxationszeitspektrum, Elastizität und Viskosität von Kautschuk IHelvetica Chimica Acta, 30
(1990)
Integro-differential equations which interpolate the heat equation and the wave equation
F. Steutel (1972)
Preservation of infinite divisibility under mixing and related topics, 33
Yanghua Wang, Jian Guo (2004)
Modified Kolsky model for seismic attenuation and dispersionJournal of Geophysics and Engineering, 1
M. Caputo (1967)
Linear Models of Dissipation whose Q is almost Frequency Independent-IIGeophysical Journal International, 13
J. Geluk, L.F.M. deHaan (1987)
Regular variation, extensions and Tauberian theorems, 40
Asymptotic wavefront expansions in hereditary media with singular memory kernels
W. Wyss (1986)
The fractional diffusion equationJournal of Mathematical Physics, 27
Andrzej Hanygad (2002)
Multidimensional solutions of time-fractional diffusion-wave equationsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458
Helly (1936)
Fourier transforms in the complex domainMonatshefte für Mathematik und Physik, 44
A. Kreis, A. Pipkin (1986)
Viscoelastic pulse propagation and stable probability distributionsQuarterly of Applied Mathematics, 44
M. Caputo (1966)
Linear models of dissipation whose Q is almost frequency independentAnnals of Geophysics, 19
H. Engler (2005)
Asymptotic Self-Similarity for Solutions of Partial Integro-Differential EquationsZeitschrift Fur Analysis Und Ihre Anwendungen, 26
Anders Jessen, T. Mikosch (2006)
Regularly varying functionsPublications De L'institut Mathematique, 80
E. Kjartansson (1979)
Constant Q-wave propagation and attenuationJournal of Geophysical Research, 84
C. Lomnitz (1957)
Linear Dissipation in SolidsJournal of Applied Physics, 28
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.
The Quarterly Journal of Mechanics and Applied Mathematics – Oxford University Press
Published: Mar 7, 2007
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.