论文标题
经典热弹性系统的大型渐近行为
Large-time asymptotic behaviors for the classical thermoelastic system
论文作者
论文摘要
在本文中，我们在整个空间中使用傅立叶热传导定律研究了经典的热弹性系统，$ \ mathbb {r}^n $当$ n = 1,2,3 $，尤其是，尤其是，其弹性位移的渐近概况。当$ n = 1,2 $时，我们发现了弹性位移的最佳增长估计，其增长率与自由波模型的增长率一致，而当$ n = 3 $时，最佳衰减速率与高斯内核有关。此外，在加权基准的新条件下，首先由扩散波，热核和奇异组件的组合引入了大型最佳领先术语。我们还用加权$ l^1 $ Datum作为副产品说明了解决方案的二阶轮廓。这些结果表明，波浪结构仅适用于一维热弹性系统。
In this paper, we study the classical thermoelastic system with Fourier's law of heat conduction in the whole space $\mathbb{R}^n$ when $n=1,2,3$, particularly, asymptotic profiles for its elastic displacement as large-time. We discover optimal growth estimates of the elastic displacement when $n=1,2$, whose growth rates coincide with those for the free wave model, whereas when $n=3$ the optimal decay rate is related to the Gaussian kernel. Furthermore, under a new condition for weighted datum, the large-time optimal leading term is firstly introduced by the combination of diffusion-waves, the heat kernel and singular components. We also illustrate a second-order profile of solution by diffusion-waves with weighted $L^1$ datum as a by-product. These results imply that wave-structure large-time behaviors hold only for the one- and two-dimensional thermoelastic systems.
