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

2018/01/09 by Han, Qing, Zhang, Lin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.02795

Abstract

We study the linear wave equation \Box_gu=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 τ=0 and a boundary value on the timelike surface r=r₀. We obtain spacetime H^p-estimates of ru for r>r₀ and derive an asymptotic exapnsion of ru in terms of 1/r as r→∞.

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