Asymptotics for Null-timelike Boundary Problems for General Linear Wave Equations

Qing Han; Lin Zhang

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arXiv · 1801.02795

Asymptotics for Null-timelike Boundary Problems for General Linear Wave Equations

Qing Han·Lin Zhang

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Abstract

We study the linear wave equation $\Box_{g}u=0$ in Bondi-Sachs coordinates, for an asymptotically flat Lorentz metric $g$. We consider the null-timelike boundary problem, where an initial value is given on the null surface $\tau=0$ and a boundary value on the timelike surface $r=r_{0}$. We obtain spacetime $H^{p}$-estimates of $ru$ for $r>r_0$ and derive an asymptotic exapnsion of $ru$ in terms of ${1}/{r}$ as $r\to\infty$.

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Qing Han, Lin Zhang. 2018-01-09. Asymptotics for Null-timelike Boundary Problems for General Linear Wave Equations. https://arxiv.org/abs/1801.02795

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