Local energy decay for linear wave equations with variable coefficients |
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Authors: | Ryo Ikehata |
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Institution: | Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan |
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Abstract: | A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489]. |
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Keywords: | Wave equation Variable coefficients Star-shaped Local energy decay Noncompactly supported initial data |
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