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

DOI:
https://doi.org/10.1090/S0002-9947-09-04742-4

Published electronically:
December 14, 2009

MathSciNet review:
2584601

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We establish weighted 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 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:
https://doi.org/10.1090/S0002-9947-09-04742-4

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.