Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The non-uniform motion of a thin smooth rigid inclusion through an elastic solid

Author: L. M. Brock
Journal: Quart. Appl. Math. 36 (1978), 269-277
MSC: Primary 73.35; Secondary 35C99
DOI: https://doi.org/10.1090/qam/521409
MathSciNet review: 521409
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Abstract: A two-dimensional example of non-uniform motion by a smooth, relatively thin, symmetric rigid inclusion through an elastic solid is analyzed. Integral solutions to the related boundary-initial value problem are obtained for the case of edge speeds bounded by the dilatational wave speed at large times. The wavefront patterns, including the possibility of Mach waves, are noted. Some attention is focused on the case of the straight wedge, and logarithmic singularities are found at its edge for subsonic speeds.

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DOI: https://doi.org/10.1090/qam/521409
Article copyright: © Copyright 1978 American Mathematical Society

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