Precise decay rate estimates for time-dependent dissipative systems |
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Authors: | Patrick Martinez |
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Institution: | (1) Département de Mathématiques, E. N. S. Cachan Antenne de Bretagne, Campus de Ker Lann, 35 170 Bruz, France |
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Abstract: | We consider the wave equation damped with a nonlinear time-dependent distributed dissipation. By generalizing a method recently
introduced to study autonomous systems, we show that the energy of the system decays to zero with an explicit and precise
decay rate estimate under sharp assumptions on the feedback. Then we prove that our estimates are optimal for the problem
of the one dimensional wave equation damped by a nonlinear time-dependent boundary feedback. This extends and improves several
earlier results of E. Zuazua and M. Nakao, and completes strong stability results of P. Pucci and J. Serrin. |
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Keywords: | |
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