Long-time effect of relaxation for hyperbolic conservation laws
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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.
KeywordsNeural Network Complex System Initial Data Nonlinear Dynamics Convergence Rate
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