In this report we obtain higher order asymptotic expansions of solutions to wave equations with frictional and viscoelastic damping terms. Although the diffusion phenomena are dominant, differences between the solutions we deal with and those of heat equations can be seen by comparing the second order expansions of them. In order to analyze such effects we consider the weighted L 1 initial data. We also give some lower bounds which show the optimality of obtained expansions.
In this paper we obtain the precise description of the asymptotic behavior of the solution u ofwe develop the arguments in [15] and [18] and establish a method to obtain the asymptotic expansions of the solutions to a nonlinear fractional diffusion equationwhere 0 < θ < 2 and p > 1 + θ/N .
We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We will derive asymptotic profiles of the solution in L 2 -sense as t → ∞ in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit expression of the solution (high frequency estimates) and the method due to [10] (low frequency estimates).
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