Communications in Mathematical Physics

, Volume 172, Issue 1, pp 39–55 | Cite as

Long-time effect of relaxation for hyperbolic conservation laws

  • I-Liang Chern
Article

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 theL p -sense for 1≦p≦∞ is also obtained and this rate is optimal.

Keywords

Neural Network Complex System Initial Data Nonlinear Dynamics Convergence Rate 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • I-Liang Chern
    • 1
  1. 1.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan, R.O.C.

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