The Energy Decay of Solutions to the Initial-Boundary Value Problem for the Wave Equation in an Inhomogeneous Medium
[Technical Report, Research Report]
NEW YORK UNIV NY
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The paper is concerned with the decay of the energy of disturbances which are propagated according to the wave equation with variable index of refraction in the exterior of a finite star-shaped reflecting body. It is shown that the energy of the disturbance decays like some power of t to the minus 1. Certain conditions of growth and continuity are made on the index in order to insure some decay factor. The energy decay is obtained by estimating the solution of an integral equation which results when one applies the Friedrichs A-B-C method to the modified wave equation operator. Using the energy estimate with other familiar estimates, one obtains a rate of decay for the disturbance itself.
- Line, Surface and Bulk Acoustic Wave Devices
- Numerical Mathematics