## Sharp polynomial decay rates for the damped wave equation with Hölder-like damping

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- by Kiril Datchev and Perry Kleinhenz
- Proc. Amer. Math. Soc.
**148**(2020), 3417-3425 - DOI: https://doi.org/10.1090/proc/15018
- Published electronically: May 8, 2020
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## Abstract:

We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta }$ near the boundary of the support and show decay at rate $1/t^{\frac {\beta +2}{\beta +3}}$. In the case where $W$ vanishes exactly like $x^{\beta }$ this result is optimal by [Comm. Math. Phys. 369 (2019), pp. 1187–1205]. The proof uses a version of the Morawetz multiplier method.## References

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## Bibliographic Information

**Kiril Datchev**- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 860651
- Email: kdatchev@purdue.edu
**Perry Kleinhenz**- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- MR Author ID: 1329164
- Email: pbk@math.northwestern.edu
- Received by editor(s): September 6, 2019
- Received by editor(s) in revised form: December 18, 2019
- Published electronically: May 8, 2020
- Additional Notes: The first author was partially supported by NSF Grant DMS-1708511.

The second author was partially supported by the National Science Foundation grant RTG: Analysis on Manifolds at Northwestern University. - Communicated by: Ariel Barton
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 3417-3425 - MSC (2010): Primary 35L05, 47A10
- DOI: https://doi.org/10.1090/proc/15018
- MathSciNet review: 4108848