Decay estimates for wave equations with variable coefficients

Radu, Petronela; Todorova, Grozdena; Yordanov, Borislav

doi:10.1090/S0002-9947-09-04742-4

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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