Global asymptotic stability of the rarefaction waves to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation laws
Global asymptotic stability of the rarefaction waves to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation laws
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DOI：
10.3934/cpaa.2023011
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发表时间：
2022
影响因子：
1
通讯作者：
Natsumi Yoshida
中科院分区：
文献类型：
--
作者：
Natsumi Yoshida
在这篇文章中，我们研究了标量扩散色散守恒律的柯西问题解的渐近行为。特别是，我们处理了色散通量不包括粘性通量的情况，即非粘性扩散通量的情况。当双曲部分相应的黎曼问题存在由单个稀疏波组成的黎曼解时，证明了柯西问题的解随着时间的推移趋于稀疏波。
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar diffusive dispersive conservation laws where the far field states are prescribed. Especially, we deal with the case where the dispersive flux does not consist of viscous flux, that is, non-viscous diffusive flux. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity.