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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Decay estimates for wave equations with variable coefficients
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by Petronela Radu, Grozdena Todorova and Borislav Yordanov PDF
Trans. Amer. Math. Soc. 362 (2010), 2279-2299 Request permission

Abstract:

We establish weighted $L^2-$estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the $L^2-$norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.
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Additional Information
  • Petronela Radu
  • Affiliation: Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588
  • Email: pradu@math.unl.edu
  • Grozdena Todorova
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Knoxville, Tennessee 37996
  • Email: todorova@math.utk.edu
  • Borislav Yordanov
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Knoxville, Tennessee 37996
  • Email: yordanov@math.utk.edu
  • Received by editor(s): October 4, 2007
  • Published electronically: December 14, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2279-2299
  • MSC (2000): Primary 35L05, 35L15; Secondary 37L15
  • DOI: https://doi.org/10.1090/S0002-9947-09-04742-4
  • MathSciNet review: 2584601