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Large time behavior of entropy solutions to some hyperbolic system with dissipative structure

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Abstract

In this paper the large time behavior of the global L ∞ entropy solutions to the hyperbolic system with dissipative structure is investigated. It is proved that as t → ∞ the entropy solutions tend to a constant equilibrium state in L 2 norm with exponential decay even when the initial values are arbitrarily large. As an illustration, a class of 2 × 2 system is studied.

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Authors and Affiliations

  1. Department of Mathematics, Shandong Normal University, Jinan, 250014, China

    Hui-min Yu

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  1. Hui-min Yu
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Correspondence to Hui-min Yu.

Additional information

This project is supported by the National Natural Science Foundation of China (Grant No. 10901095) and the Promotive Research Fund for Excellent Young and Middle-Aged Scientists of Shandong Province (Grant No. BS2010SF025).

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Yu, Hm. Large time behavior of entropy solutions to some hyperbolic system with dissipative structure. Acta Math. Appl. Sin. Engl. Ser. 29, 509–516 (2013). https://doi.org/10.1007/s10255-011-0097-3

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  • DOI: https://doi.org/10.1007/s10255-011-0097-3

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