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

Kenigson Jessica S. | Zendy; Kenigson Jonathan J. | Zendy

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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.

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