Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Sharp polynomial decay rates for the damped wave equation with Hölder-like damping
HTML articles powered by AMS MathViewer

by Kiril Datchev and Perry Kleinhenz PDF
Proc. Amer. Math. Soc. 148 (2020), 3417-3425 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35L05, 47A10
  • Retrieve articles in all journals with MSC (2010): 35L05, 47A10
Additional 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