Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion

Shuichi Kawashima*, Akitaka Matsumura

*この研究の対応する著者

研究成果: Article査読

277 被引用数 (Scopus)

抄録

The asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics. 1) The solution of a scalar conservation law with viscosity approaches the traveling wave solution at the rate t (for some γ>0) as t→∞, provided that the initial disturbance is small and of integral zero, and in addition decays at an algebraic rate for |x|→∞. 2) The traveling wave solution with Nishida and Smoller's condition of the system of a viscous heat-conductive ideal gas is asymptotically stable, provided the initial disturbance is small and of integral zero. 3) The traveling wave solution with weak shock profile of the Broadwell model system of the Boltzmann equation is asymptotically stable, provided the initial disturbance is small and its hydrodynamical moments are of integral zero. Each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one. The property of integral zero of the initial disturbance plays a crucial role in this procedure.

本文言語English
ページ(範囲)97-127
ページ数31
ジャーナルCommunications in Mathematical Physics
101
1
DOI
出版ステータスPublished - 1985 3月
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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