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The $L^p$ Stability of Relaxation Rarefaction Profiles

by Liu, Hailiang.

Series: 1999-24, Preprints

35L45 Initial value problems for first-order hyperbolic systems
35L65 Conservation laws
35B40 Asymptotic behavior of solutions

We consider the large time behavior of solutions for a
hyperbolic relaxation system. For a certain class of
initial data the solution is shown to converge to relaxation
rarefaction profiles at a determined asymptotic rate.
The result is established without the smallness conditions
of the wave strength and the initial disturbances.

Decay rate, rarefaction wave, relaxation