## In this paper, we consider wave equations with double damping terms expressed by $$u_{t}$$ut and $$-\Delta u_{t}$$-Δut and a power type of nonlinearity $$\vert u\vert ^{p}$$|u|p. 在本文中，我们考虑具有由 $$u_{t}$$ut 和 $$-\Delta u_{t}$$-Δut 表示的双阻尼项的波动方程以及非线性的幂类型 $$\vert u\vert ^{p}$$|u|p.

Critical exponent for semi-linear wave equations with double damping terms in exterior domains

## We consider the Cauchy problem in \begin{document}${\bf R}^{n}$\end{document} for some wave equations with double damping terms, that is, one is the frictional damping \begin{document}$u_{t}(t, x)$\end{document} and the other is very strong structural damping expressed as \begin{document}$(-\Delta)^{\theta}u_{t}(t, x)$\end{document} with \begin{document}$\theta > 1$\end{document}. 我们考虑 \begin{document}${\bf R}^{n}$\end{document} 中的柯西问题，对于一些具有双阻尼项的波动方程，即一个是摩擦阻尼 \begin{document}$u_{t}(t, x)$\end{document} 和另一个是非常强的结构阻尼，表示为 \begin{document}$(-\Delta)^{\theta}u_{t}(t, x)$\end{document} 与 \begin{document}$\theta > 1$\end{document}。

Optimal energy decay rates for some wave equations with double damping terms

## In this article, we study semi-linear $\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\sigma\ge 1$. 在本文中，我们研究了具有双阻尼的半线性 $\sigma$-演化方程，包括任意 $\sigma\ge 1$ 的摩擦阻尼和粘弹性阻尼。

Study of semi-linear $\sigma$-evolution equations with frictional and visco-elastic damping.