论文标题
摩尔 - 吉布森 - 汤普森方程的奇异热弛豫极限在传播声波传播时产生
Singular Thermal Relaxation Limit for the Moore-Gibson-Thompson Equation Arising in Propagation of Acoustic Waves
论文作者
论文摘要
考虑了描述异质介质中的声波的摩尔 - 吉布森 - 汤普森（MGT）方程。这些是主要双曲线类型的时间演变。 MGT模型是由于在三阶时间派生的前面出现热弛豫系数τ{>} {0}而导致有限速度传播的。由于τ的值相对较小，而且通常可以忽略不计，因此在τ{\ to} {0}时了解模型的渐近行为和特征很重要。这是一个特别精致的问题，因为τ-Dynamics由一个单数为τ{\ to} {0}的发电机控制。事实证明，极限动力学对应于抛物线类型的线性化Westervelt方程。在本文中，我们对渐近学进行了严格的分析，其中包括无限范围内相应发展的强烈收敛。这是通过研究收敛速率以及三阶进化的统一指数稳定性而获得的。还将提供对MGT方程式的光谱分析，以及对两个方程式（MGT和线性化Westervelt）的光谱上限的讨论。
Moore-Gibson-Thompson (MGT) equations, which describe acoustic waves in a heterogeneous medium, are considered. These are the third order in time evolutions of a predominantly hyperbolic type. MGT models account for a finite speed propagation due to the appearance of thermal relaxation coefficient τ {>} {0} in front of the third order time derivative. Since the values of τ are relatively small and often negligible, it is important to understand the asymptotic behavior and characteristics of the model when τ {\to} {0}. This is a particularly delicate issue since the τ- dynamics is governed by a generator which is singular as τ {\to} {0}. It turns out that the limit dynamics corresponds to the linearized Westervelt equation which is of a parabolic type. In this paper, we provide a rigorous analysis of the asymptotics which includes strong convergence of the corresponding evolutions over infinite horizon. This is obtained by studying convergence rates along with the uniform exponential stability of the third order evolutions. Spectral analysis for the MGT-equation along with a discussion of spectral uppersemicontinuity for both equations (MGT and linearized Westervelt) will also be provided.
