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

Hanche-Olsen, Harald; Holden, Helge; Risebro, Nils Henrik

doi:10.1090/qam/1939007

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 $4 \times 4$ system of conservation laws that is linearly degenerate in all wave families. Conservation of energy leads to ${L^{2}}$ estimates that are used in the analysis.

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