Unimodality and viscoelastic pulse propagation
Author:
Gustaf Gripenberg
Journal:
Quart. Appl. Math. 51 (1993), 183-189
MSC:
Primary 73F15; Secondary 45K05
DOI:
https://doi.org/10.1090/qam/1205945
MathSciNet review:
MR1205945
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Abstract: Sufficient conditions on the stress relaxation modulus in a viscoelastic material are given in order for initially short mechanical pulses in the material to remain unimodal.
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H. Kolsky, The propagation of stress pulses in viscoelastic solids, Philos. Mag., Ser. 8 1, 693–710 (1956)
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A. C. Pipkin, Lectures on Viscoelasticity Theory, 2nd ed., Springer, New York, 1986
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- Stephen James Wolfe, On the unimodality of $L$ functions, Ann. Math. Statist. 42 (1971), 912–918. MR 278357, DOI https://doi.org/10.1214/aoms/1177693320
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Y. Fujita, Integrodifferential equation which interpolates the heat equation and the wave equation, Osaka J. Math. 27, 309–321 (1990)
G. Gripenberg, S-O. Londen, and O. Staffans, Volterra Integral and Functional Equations, Cambridge University Press, Cambridge, 1990
I. A. Ibragimov, On the composition of unimodal distributions, Theory Probab. Appl. 1, 255–260 (1956)
H. Kolsky, The propagation of stress pulses in viscoelastic solids, Philos. Mag., Ser. 8 1, 693–710 (1956)
A. Kreis, and A. C. Pipkin, Viscoelastic pulse propagation and stable probability distributions, Quart. Appl. Math. XLIV, 353–360 (1986)
A. C. Pipkin, Lectures on Viscoelasticity Theory, 2nd ed., Springer, New York, 1986
J. Prüss, Positivity and regularity of hyperbolic Volterra equations in Banach spaces, Math. Ann. 279, 317–344 (1987)
M. Renardy, W. J. Hrusa, and J. A. Nohel, Mathematical Problems in Viscoelasticity, Longman, London, 1987
S. J. Wolfe, On the unimodality of L functions, Ann. Math. Statist. 42, 912–918 (1971)
M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probab. 6, 523–531 (1978)
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Article copyright:
© Copyright 1993
American Mathematical Society
