Preprint 2000-014

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

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:

Available as PostScript (448 Kbytes) or gzipped PostScript (188 Kbytes; uncompress using gunzip).

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).

Comments:

Submitted by:

<hanche@math.ntnu.no> April 21 2000.