On the rate of decay of solutions to linear viscoelastic equation

By Yoshihiro Shibata. 2000

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5e42f7977d79f7478193fd54da7aef481c0a4472

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Semilinear structural damped waves (2012, background): “Then the following estimates can be concluded from [1]: k@ j t@x E0.”
Energy decay estimates for wave equations with a fractional damping (2012, background): “This property was first pointed out in Shibata [24] in the case when θ = 1.”
Asymptotic Profiles of Solutions for Structural Damped Wave Equations (2016, background): “, strong damping case) one should make mention to some pioneering decay estimates of solutions due to Ponce [16] and Shibata [17], in which Ponce [16] dealt with rather special initial data such as u1(x) = ∂xv(x) to avoid some singularity, and Shibata [17] has established Lp-Lq decay estimates of so”
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.”
A classification of structural dissipations for evolution operators (2016, background): “In the case of wave equation with visco-elastic damping [15, 16], that is, ı D 1 in (10), the asymptotic profile to (1) has been investigated in [17, 18].”
New decay estimates for linear damped wave equations and its application to nonlinear problem (2004, unknown): “In Reference [12] Shibata studied the Lp–Lq estimates of solutions to the Cauchy problem in RN of the linear viscoelastic equation: vtt − v− vt =0 The work of Reference [12] also was done through the Fourier transform.”
L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models (2013, background): “In both cases Lp−Lq estimates for the solutions are well understood; see [4–7, 10] and [11] for the case σ = 0 (linear or semi-linear models) and [8] for the case σ = 1.”