论文标题
与规律性损失结构的双曲线 - 羟基蛋白耦合系统的较大时间行为
Large time behavior for the hyperbolic-parabolic coupled system with the regularity-loss structure
论文作者
论文摘要
本文考虑了由广义热弹性耦合系统引起的双曲 - 抛物线耦合系统，在整个空间$ \ mathbb {r}^n $中。我们通过对角度化程序研究了一些定性特性，并通过WKB分析研究解决方案。特别是，我们通过规律性损失结构（来自Biharmonic抛物管方程和带有Riesz势能操作员的扩散波方程）和最佳衰减估计值的新大型渐近型概况（来自Biharmonic抛物管方程式和扩散波方程），适合Cauchy数据的较高规律性。最后，我们发现带有RIESZ电位耗散的波方程是我们双曲 - 促支持者耦合系统的近似模型。
This paper considers the hyperbolic-parabolic coupled system, arising from the generalized thermoelastic coupled system, in the whole space $\mathbb{R}^n$. We study some qualitative properties for an energy term by diagonalization procedures, and for the solution by the WKB analysis. Particularly, we derive new large time asymptotic profiles with the regularity-loss structure (from the biharmonic parabolic equation and the diffusion wave equation with the Riesz potential operator) and optimal decay estimates with suitable higher regularities for the Cauchy data. Finally, we discover that the wave equation with the Riesz potential dissipation is a large time approximated model of our hyperbolic-parabolic coupled system.
