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Long-time effect of relaxation for hyperbolic conservation laws

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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.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, Taiwan, R.O.C.

    I-Liang Chern

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  1. I-Liang Chern
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Communicated by S.-T. Yau

This work was supported by the National Science Council of the Republic of China under Contract NSC82-0208-M002-093

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Chern, IL. Long-time effect of relaxation for hyperbolic conservation laws. Commun.Math. Phys. 172, 39–55 (1995). https://doi.org/10.1007/BF02104510

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  • DOI: https://doi.org/10.1007/BF02104510

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