On wave propagation in linear viscoelasticity

Authors:
W. J. Hrusa and M. Renardy

Journal:
Quart. Appl. Math. **43** (1985), 237-254

MSC:
Primary 45K05; Secondary 73F99

DOI:
https://doi.org/10.1090/qam/793532

MathSciNet review:
793532

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Abstract | References | Similar Articles | Additional Information

Abstract: We discuss the initial value problem in one-dimensional linear visco-elasticity with a step-jump in the initial data. If the memory kernel is sufficiently smooth on , the solution exhibits discontinuities propagating along characteristics and a (higher order) stationary discontinuity at the position of the original step-jump. For a singular memory kernel, the propagating waves are smoothed in a manner depending on the nature of the singularity in the kernel, but the stationary discontinuity remains. We also discuss the effects of these phenomena on the regularity of solutions with arbitrary initial data.

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DOI:
https://doi.org/10.1090/qam/793532

Article copyright:
© Copyright 1985
American Mathematical Society