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Energy decay estimates for the dissipative wave equation with space–time dependent potential
Author(s) -
Kenigson Jessica S.,
Kenigson Jonathan J.
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1330
Subject(s) - dissipative system , norm (philosophy) , space time , mathematics , wave equation , fourier transform , space (punctuation) , energy (signal processing) , mathematical analysis , spacetime , physics , quantum mechanics , statistics , computer science , chemistry , political science , law , operating system
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 space–time‐dependent potential. Copyright © 2010 John Wiley & Sons, Ltd.