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Perturbation of rarefaction waves

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Abstract

Consider a pair of genuinely nonlinear strictly hyperbolic conservation lawsU t +F(U) x =0 with initial dataU(O,X)=U o (X). Suppose that the initial dataU o (X)=U 1 (X)+U 2 (X), whereU 1 (X) will issue rarefaction waves only,U 2 (X) has any finite total variation and sufficiently small deviation. We prove that the Cauchy problem has a global solution.

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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, Zhongshan, China

    Lin Longwei & Xie Feipeng

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  1. Lin Longwei
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  2. Xie Feipeng
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This work is supported in part by the Foudation of Zhongshan University Advanced Research Centre.

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Longwei, L., Feipeng, X. Perturbation of rarefaction waves. Acta Mathematica Sinica 8, 122–134 (1992). https://doi.org/10.1007/BF02629933

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  • DOI: https://doi.org/10.1007/BF02629933

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