Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
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DOI：
10.1007/bf01212358
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发表时间：
1985-03
影响因子：
2.4
通讯作者：
S. Kawashima;A. Matsumura
中科院分区：
文献类型：
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作者：
S. Kawashima;A. Matsumura
研究了几种气体动力学系统的行波解的渐近稳定性。1)当初始扰动较小且积分为0时，具有黏性的标量守恒律的解以速率- γ（对于某γ>0） ast→∞逼近行波解，且在|x|→∞时以代数速率衰减。2)具有Nishida和Smoller条件的粘性导热理想气体系统的行波解在初始扰动较小且积分为零的情况下是渐近稳定的。3)当初始扰动较小且其流体动力矩为积分零时，玻尔兹曼方程的Broadwell模型系统具有弱激波剖面的行波解渐近稳定。每个证明都是通过将初等能量法应用于原始守恒形式的集成系统来给出的。初始扰动的积分为零的性质在此过程中起着至关重要的作用。
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 ratet−γ(for someγ>0) ast→∞, 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.