Energy decay estimates for wave equations with a fractional damping

By Ryo Ikehata, Masatoshi Natsume. Differential and Integral Equations, 2012

64 citations recorded by the source corpus.

We consider the Cauchy problem in ${\bf R}^{n}$ for wave equations with a fractional damping. We generalize partially the previous results due to[12], and derive sharp decay estimates for the total energy and the $L^{2}$-norm of solutions based on the energy method in the Fourier space.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8e2d831491b61db8b5bda28686b7b6f188ec8feb

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Local and global smoothing effects for some linear hyperbolic equations with a strong dissipation (2014, background): “The interested reader is referred to [29, 19, 20, 21] and to the references quoted therein.”
Asymptotic Profiles of Solutions for Structural Damped Wave Equations (2016, methodology): “kehata [9] re-studied the problem (1.1) with σ = 1 to observe optimal decay estimates of solutions in terms of L2-norm. The result of [9] has its motivation in [12], and especially in Ikehata-Natsume [10], in there they studied more precise decay estimates of the total energy and L2-norm of solution”
The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, background): “The Cauchy problem for the viscoelastic damped wave equation has been deeply studied in [49, 31, 13, 26, 27, 29, 3, 2] and references therein.”