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arXiv · 0911.3174

Decay estimates for the one-dimensional wave equation with an inverse power potential

Roland Donninger·Wilhelm Schlag
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Abstract

We study the wave equation on the real line with a potential that falls off like $|x|^{-α}$ for $|x| \to \infty$ where $2 < α\leq 4$. We prove that the solution decays pointwise like $t^{-α}$ as $t \to \infty$ provided that there are no resonances at zero energy and no bound states. As an application we consider the $\ell=0$ Price Law for Schwarzschild black holes. This paper is part of our investigations into decay of linear waves on a Schwarzschild background.

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Roland Donninger, Wilhelm Schlag. 2010-03-10. Decay estimates for the one-dimensional wave equation with an inverse power potential. https://doi.org/10.1093/imrn%2Frnq038

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