标题： 关于带有广义双阻尼的$σ$-演化方程解的渐近性质 显示英文标题

标题： On asymptotic properties of solutions to $σ$-evolution equations with general double damping

摘要： 在本文中，我们想考虑半线性$\sigma$-演化方程的柯西问题，该方程具有双结构阻尼，对于任何$\sigma\ge 1$。 本工作的主要目的是不仅研究相应线性方程解的渐近轮廓，而且描述从半线性方程中得到的整体解的大时间行为。 我们要强调的是，新的贡献是找出对应于$\sigma_1 \in [0,\sigma/2)$的“类似抛物模型”和对应于$\sigma_2 \in (\sigma/2,\sigma]$的“$\sigma$-演化类似模型”之间的精确相互作用，这些相互作用共同出现在一个方程中。 在这方面，我们清楚地理解每个阻尼项如何影响解的渐近性质。 显示英文摘要

摘要： In this paper, we would like to consider the Cauchy problem for semi-linear $\sigma$-evolution equations with double structural damping for any $\sigma\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models" corresponding to $\sigma_1 \in [0,\sigma/2)$ and ``$\sigma$-evolution like models" corresponding to $\sigma_2 \in (\sigma/2,\sigma]$, which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.