SIAM Journal on Applied Mathematics, Volume 81, Issue 4, Page 1461-1482, January 2021.
We analyze the behavior of third-order-in-time linear and nonlinear sound waves in thermally relaxing fluids and gases as the sound diffusivity vanishes. The nonlinear acoustic propagation is modeled by the Jordan--Moore--Gibson--Thompson equation both in its Westervelt-type and in its Kuznetsov-type forms, that is, including general nonlinearities of quadratic type. As it turns out, sufficiently smooth solutions of these equations converge in the energy norm to the solutions of the corresponding inviscid models at a linear rate. Numerical experiments illustrate our theoretical findings.

中文翻译：

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三阶线性和非线性声学方程的无粘极限

SIAM Journal on Applied Mathematics，第 81 卷，第 4 期，第 1461-1482 页，2021 年 1 月。
我们分析了随着声音扩散率的消失，热弛豫流体和气体中三阶时间线性和非线性声波的行为。非线性声传播由 Jordan--Moore--Gibson--Thompson 方程以 Westervelt 型和 Kuznetsov 型形式建模，即包括二次型的一般非线性。事实证明，这些方程的足够平滑的解在能量范数中以线性速率收敛到相应无粘性模型的解。数值实验说明了我们的理论发现。