On wave propagation in linear viscoelasticity

Hrusa, W. J.; Renardy, M.

doi:10.1090/qam/793532

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: 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 $\left [ {0,\infty } \right )$, 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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