A note on the stability of the rarefaction wave of the Burgers equation

  • Youichi Hattori
  • Kenji Nishihara

DOI: 10.1007/BF03167186

Cite this article as:
Hattori, Y. & Nishihara, K. Japan J. Indust. Appl. Math. (1991) 8: 85. doi:10.1007/BF03167186


This paper is concerned with the asymptotic behavior toward the rarefaction waveuR(x/t) of the solution of the Burgers equation with viscosity. If the initial data are suitably close to constant stateu± atx=±∞, then the solutionu(x, t), roughly speaking, satisfies supR |uuR| ∼t−1/2 ast → ∞ and, except for the “neighborhoods” of the corners,x=u±t ofuR, sup |uuR|∼t−1. In the proof the exact forms ofu are available.

Key words

rarefaction wave Hopf transformation asymptotic behavior 

Copyright information

© JJIAM Publishing Committee 1991

Authors and Affiliations

  • Youichi Hattori
    • 1
  • Kenji Nishihara
    • 2
  1. 1.Yamato LaboratoryIBM JapanKanagawaJapan
  2. 2.School of Political Science and EconomicsWaseda UniversityTokyoJapan

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