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Convergence to diffusion waves of solutions for viscous conservation laws

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Abstract

We study the large-time behavior of solutions of viscous conservation laws. It is shown that solutions tend to diffusion waves, which are constructed based on the heat equation and Burgers equation. The convergence is in theL p , 1≦p≦∞ sense and is obtained as a consequence of theL 2 decay of the difference between the solution and its asymptotic state of diffusion waves.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taiwan, R.O.C.

    I.-Liang Chern

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

    Tai-Ping Liu

Authors
  1. I.-Liang Chern
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  2. Tai-Ping Liu
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Additional information

Communicated by A. Jaffe

Supported by the National Sciences Council of the Republic of China under the contract NSC-76-0208-M-001-09

Supported by NSF under Grant No. DMS-84-01355

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Chern, IL., Liu, TP. Convergence to diffusion waves of solutions for viscous conservation laws. Commun.Math. Phys. 110, 503–517 (1987). https://doi.org/10.1007/BF01212425

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  • DOI: https://doi.org/10.1007/BF01212425

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