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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Decay estimates for wave equations with variable coefficients


Authors: Petronela Radu, Grozdena Todorova and Borislav Yordanov
Journal: Trans. Amer. Math. Soc. 362 (2010), 2279-2299
MSC (2000): Primary 35L05, 35L15; Secondary 37L15
Published electronically: December 14, 2009
MathSciNet review: 2584601
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04742-4
PII: S 0002-9947(09)04742-4
Keywords: Wave equations with variable coefficients, linear dissipation, decay rates, subsolution
Received by editor(s): October 4, 2007
Published electronically: December 14, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.