标题： 结构阻尼波动方程解的渐近轮廓 显示英文标题

标题： Asymptotic profiles of solutions for structural damped wave equations

摘要： 在本文中，我们获得了结构阻尼波动方程$\partial_{t}^{2} u - \Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$的柯西问题解的几个渐近轮廓，其中$\nu >0$和$0< \sigma \le1$。我们的结果是解的近似公式，该公式为一个特殊函数的常数倍，当$t \to \infty$时成立，这表明解的渐近轮廓根据值$\nu$和$\sigma$被分类为$5$种模式。 显示英文摘要

摘要： In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u - \Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0< \sigma \le1$. Our result is the approximation formula of the solution by a constant multiple of a special function as $t \to \infty$, which states that the asymptotic profiles of the solutions are classified into $5$ patterns depending on the values $\nu$ and $\sigma$.