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Energy decay estimates for the dissipative wave equation with space–time dependent potential

✍ Scribed by Jessica S. Kenigson; Jonathan J. Kenigson

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
209 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

We study the asymptotic behavior of solutions of dissipative wave equations with space-time-dependent potential. When the potential is only time-dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space-dependent, a powerful technique has been developed by Todorova and Yordanov to capture the exact decay of solutions. The presence of a space-time-dependent potential, as in our case, requires modifications of this technique. We find the energy decay and decay of the L 2 norm of solutions in the case of spacetime-dependent potential.

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