$L^2$ asymptotic profiles of solutions to linear damped wave equations

Hironori Michihisa

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arXiv · 1710.04870

$L^2$ asymptotic profiles of solutions to linear damped wave equations

Hironori Michihisa

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Abstract

In this paper we obtain higher order asymptotic profilles of solutions to the Cauchy problem of the linear damped wave equation in $\textbf{R}^n$ \begin{equation*} u_{tt}-\Delta u+u_t=0, \qquad u(0,x)=u_0(x), \quad u_t(0,x)=u_1(x), \end{equation*} where $n\in\textbf{N}$ and $u_0$, $u_1\in L^2(\textbf{R}^n)$. Established hyperbolic part of asymptotic expansion seems to be new in the sense that the order of the expansion of the hyperbolic part depends on the spatial dimension.

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Hironori Michihisa. 2017-10-13. $L^2$ asymptotic profiles of solutions to linear damped wave equations. https://arxiv.org/abs/1710.04870

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