Decay estimates for one-dimensional wave equations with inverse power potentials
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- by O. Costin and M. Huang PDF
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Abstract:
We study the one-dimensional wave equation with an inverse power potential that equals $const.x^{-m}$ for large $|x|$, where $m$ is any positive integer greater than or equal to 3. We show that the solution decays pointwise like $t^{-m}$ for large $t$, which is consistent with existing mathematical and physical literature under slightly different assumptions.
Our results can be generalized to potentials consisting of a finite sum of inverse powers, the largest of which being $const.x^{-\alpha }$, where $\alpha >2$ is a real number, as well as potentials of the form $const.x^{-m}+O( x^{-m-\delta _1})$ with $\delta _1>3$.
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Additional Information
- O. Costin
- Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
- MR Author ID: 52070
- M. Huang
- Affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong
- Received by editor(s): July 19, 2013
- Received by editor(s) in revised form: October 16, 2013
- Published electronically: July 29, 2014
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 3705-3732
- MSC (2010): Primary 35L05, 35P25, 34M37, 34M40, 35Q75
- DOI: https://doi.org/10.1090/S0002-9947-2014-06345-9
- MathSciNet review: 3314821