论文标题
粘性情况下，约旦 - 摩尔 - 吉布森 - 汤普森方程的渐近行为
Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case
论文作者
论文摘要
在本文中，我们研究了非线性声学中基本模型的大型行为，正是粘性的Jordan-Moore-Gibson-Thompson（JMGT）方程在整个空间$ \ mathbb {r}^n $中。该模型描述了在不稳定流程下的完美气体中的非线性声学，并为Cattaneo的热传导定律提供了装备。通过采用精致的WKB分析和傅立叶分析，我们将溶液的一阶和二阶渐近概况得出了摩尔 - 吉布森 - 汤普森（MGT）方程为$ t \ gg 1 $，这说明了解决方案的新型最佳估计，甚至减去了其轮廓。关于非线性JMGT方程，通过建议非线性部分的新分解，我们研究了具有适当规律性的全局（及时）小数据Sobolev解决方案的存在和大型剖面。这些结果有助于桥接JMGT方程和扩散波之间的新连接，为$ t \ gg1 $。
In this paper, we study large-time behaviors for a fundamental model in nonlinear acoustics, precisely, the viscous Jordan-Moore-Gibson-Thompson (JMGT) equation in the whole space $\mathbb{R}^n$. This model describes nonlinear acoustics in perfect gases under irrotational flow and equipping Cattaneo's law of heat conduction. By employing refined WKB analysis and Fourier analysis, we derive first- and second-order asymptotic profiles of solution to the Moore-Gibson-Thompson (MGT) equation as $t\gg 1$, which illustrates novel optimal estimates for the solutions even subtracting its profiles. Concerning the nonlinear JMGT equation, via suggesting a new decomposition of nonlinear portion, we investigate the existence and large-time profiles of global (in time) small data Sobolev solutions with suitable regularity. These results help bridge a new connection between the JMGT equation and diffusion-waves as $t\gg1$.
