In this paper we obtain higher order asymptotic expansions of solutions to the Cauchy problem of the linear damped wave equation in ${\mathbf{\text{R}}}^n$$u_{tt}-\mathrm{\Delta }u+u_t=0,u(0,x)=u_0(x),u_t(0,x)=u_1(x),$ where $n\in \mathbf{\text{N}}$ and $u_0$, $u_1\in L^1({\mathbf{\text{R}}}^n)\cap L^2({\mathbf{\text{R}}}^n)$. Established hyperbolic effects seem to be new in the sense that the order of obtained expansions depends on the spatial dimension.

中文翻译：

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L ²线性阻尼波动方程解的渐近分布

在本文中，我们获得了线性阻尼波动方程的柯西问题解的高阶渐近展开式 ${\mathbf{\text{电阻}}}^n$${你}_{吨吨}-\mathrm{\Delta }你+{你}_{吨}=0,你(0,X)={你}_0(X),{你}_{吨}(0,X)={你}_1(X),$ 在哪里 $n\in \mathbf{\text{N}}$ 和 ${你}_0$, ${你}_1\in {升}^1({\mathbf{\text{电阻}}}^n)\cap {升}^2({\mathbf{\text{电阻}}}^n)$. 建立的双曲线效应似乎是新的，因为获得的扩展顺序取决于空间维度。