Long-time effect of relaxation for hyperbolic conservation laws
Journal
Communications in Mathematical Physics
Journal Volume
172
Journal Issue
1
Pages
39-55
Date Issued
1995
Author(s)
Abstract
The hyperbolic conservation laws with relaxation appear in many physical systems such as nonequilibrium gas dynamics, flood flow with friction, viscoelasticity, magnetohydrodynamics, etc. This article studies the long-time effect of relaxation when the initial data is a perturbation of an equilibrium constant state. It is shown that in this case the long-time effect of relaxation is equivalent to a viscous effect, or in other words, the Chapman-Enskog expansion is valid. It is also shown that the corresponding solution tends to a diffusion wave time asymptotically. This diffusion wave carries an invariant mass. The convergence rate to this diffusion wave in the Lp-sense for 1≦p≦∞ is also obtained and this rate is optimal. © 1995 Springer-Verlag.
SDGs
Type
journal article