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Hyperbolic conservation laws with relaxation

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Abstract

The effect of relaxation is important in many physical situations. It is present in the kinetic theory of gases, elasticity with memory, gas flow with thermo-non-equilibrium, water waves, etc. The governing equations often take the form of hyperbolic conservation laws with lower-order terms. In this article, we present and analyze a simple model of hyperbolic conservation laws with relaxation effects. Dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified. Stability criteria for diffusion waves, expansion waves and traveling waves are found and justified nonlinearly. Time-asymptotic expansion and the energy method are used in the analysis. For dissipative waves, the expansion is similar in spirit to the Chapman-Enskog expansion in the kinetic theory. For shock waves, however, a different approach is needed.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Tai-Ping Liu

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  1. Tai-Ping Liu
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Communicated by A. Jaffe

The paper was written at Mittag-Leffler Institute; the author wants to thank the Institute for the visiting position in 1986. This work was supported in part by an NSF grant

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Liu, TP. Hyperbolic conservation laws with relaxation. Commun.Math. Phys. 108, 153–175 (1987). https://doi.org/10.1007/BF01210707

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  • DOI: https://doi.org/10.1007/BF01210707

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