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Asymptotic Stability of Relaxation Shock Profiles for Hyperbolic Conservation Laws

by Liu, Hailiang.

Series: 1999-25, Preprints

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

This paper studies the asymptotic stability of traveling
relaxation shock profiles for hyperbolic systems of
conservation laws. Under a stability condition of subcharacteristic
type the large time relaxation dynamics on the level of
shocks is shown to be determined by the equilibrium conservation
lawa. The proof is due to the energy principle, using the weighted
norms, the interaction of waves from various modes is
treated by imposing suitable weight matrix.

asymptotic stability