The Riemann problem for an elastic string with a linear Hooke's law

Authors:
Harald Hanche-Olsen, Helge Holden and Nils Henrik Risebro

Journal:
Quart. Appl. Math. **60** (2002), 695-705

MSC:
Primary 35L65; Secondary 35L67, 74H45, 74K05

DOI:
https://doi.org/10.1090/qam/1939007

MathSciNet review:
MR1939007

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Abstract: We solve the Riemann problem for vibrations of an infinite, planar, perfectly elastic string with a linear relation between the string tension and the local stretching, i.e., with a linear Hooke's law. The motion is governed by a system of conservation laws that is linearly degenerate in all wave families. Conservation of energy leads to estimates that are used in the analysis.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1939007

Article copyright:
© Copyright 2002
American Mathematical Society