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Optimal energy decay rates for some wave equations with double damping terms

  • * Corresponding author: Ryo Ikehata

    * Corresponding author: Ryo Ikehata 

The first author is supported by grant-in-Aid for scientific Research (C)15K04958 of JSPS

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  • We consider the Cauchy problem in $ {\bf R}^{n} $ for some wave equations with double damping terms, that is, one is the frictional damping $ u_{t}(t, x) $ and the other is very strong structural damping expressed as $ (-\Delta)^{\theta}u_{t}(t, x) $ with $ \theta > 1 $. We will derive optimal decay rates of the total energy and the $ L^{2} $-norm of solutions as $ t \to \infty $. These results can be obtained in the case when the initial data have a sufficient high regularity in order to guarantee that the corresponding high frequency parts of such energy and $ L^{2} $-norm of solutions are remainder terms. A strategy to get such results comes from a method recently developed by the first author [11].

    Mathematics Subject Classification: Primary: 35L15, 35L05; Secondary: 35B40.


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