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

H. Hanche-Olsen, H. Holden, and N.H. Risebro

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.

Paper:
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Author(s):
H. Hanche-Olsen, <hanche@math.ntnu.no>
H. Holden, <holden@math.ntnu.no>
N.H. Risebro, <nilshr@math.uio.no>
Publishing information:
Appeared in Quarterly of Applied Mathematics 60, 695-705 (2002).