Abstract
The equations of linear viscoelasticity with a bounded memory kernel have been shown to propagate singularities in a similar way as hyperbolic equations. In this paper, we investigate a model problem for a certain class of unbounded memory kernels. It is shown thatC ∞-solutions are obtained, although there is a discontinuity in the boundary conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Coleman, B. D., M. E. Gurtin, Arch. Rational Mech. Anal.19, 239 (1965).
Curtiss, C. F., R. B. Bird, J. Chem. Phys.74, 2016 (1981).
Gradshteyn, I. S., I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, 4th ed. (New York 1980).
Kazakia, J. Y., R. S. Rivlin, Rheol. Acta20, 111 (1981).
Laun, H. M., Rheol. Acta17, 1 (1978).
Narain, A., D. D. Joseph, Rheol. Acta21, 228 (1982).
Narain, A., Ph. D. Thesis, Univ. of Minnesota (to appear).
Peetre, J., Ann. Inst. Fourier16, 279 (1966).
Saut, J. C., D. D. Joseph, Fading Memory, to appear.
Tanner, R. I., ZAMP13, 573 (1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Renardy, M. Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids. Rheol Acta 21, 251–254 (1982). https://doi.org/10.1007/BF01515713
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01515713