Electron. J. Diff. Eqns., Vol. 2006(2006), No. 116, pp. 1-8.

A Riemann problem with small viscosity and dispersion

Kayyunnapara Thomas Joseph

In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.

Submitted July 11, 2006. Published September 26, 2006.
Math Subject Classifications: 35B40, 35L65.
Key Words: Elastodynamics equation; viscosity; dispersion; Riemann problem.

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Kayyunnapara Thomas Joseph
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005, India
email: ktj@math.tifr.res.in

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