Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation

DOI10.2977/prims/1195162849zbMath0864.35066OpenAlexW2095288303MaRDI QIDQ2563730

Kiyoshi Mochizuki, Hideo Nakazawa

Publication date: 16 December 1996

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195162849

zbMATH Keywords

weighted energy inequalitycritical exponent of logarithmic order

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20)

Related Items (37)

Wave equations with time-dependent dissipation. I: Non-effective dissipation ⋮ Asymptotics for the nonlinear dissipative wave equation ⋮ Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain ⋮ Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients ⋮ Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy ⋮ Critical exponent for semilinear wave equation with critical potential ⋮ Global solvability and behavior of solutions of the Cauchy problem for a system of two semilinear hyperbolic equations with dissipation ⋮ Energy decay rate of the wave equations on Riemannian manifolds with critical potential ⋮ Decay estimates for a kind of linear wave equations ⋮ Asymptotic expansion of solutions to the wave equation with space-dependent damping ⋮ Decay property of solutions to the wave equation with space‐dependent damping, absorbing nonlinearity, and polynomially decaying data ⋮ Energy decay for wave equations with a potential and a localized damping ⋮ A uniform resolvent estimate for a Helmholtz equation with some large perturbations in an exterior domain ⋮ Optimal decay rate of the energy for wave equations with critical potential ⋮ Existence, non-existence and asymptotic behavior of global solutions to the Cauchy problem for systems of semilinear hyperbolic equations with damping terms ⋮ Unnamed Item ⋮ Critical exponent for the semilinear wave equations with a damping increasing in the far field ⋮ Energy decay for a degenerate hyperbolic equation with a dissipative term ⋮ On the asymptotic behavior of the energy for the wave equations with time depending coefficients ⋮ Energy decay for a viscoelastic wave equation with space-time potential in \(\mathbb{R}^n\) ⋮ Total energy decay for semilinear wave equations with a critical potential type of damping ⋮ On decay-nondecay and scattering for Schrödinger equations with time dependent complex potentials ⋮ Lp - Lq Decay Estimates for Wave Equations with Time-Dependent Coefficients ⋮ Energy decay rates of elastic waves in unbounded domain with potential type of damping ⋮ On diffusion phenomena for the linear wave equation with space-dependent damping ⋮ Existence and non-existence of global solutions of the Cauchy problem for higher order semilinear pseudo-hyperbolic equations ⋮ Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term ⋮ Scattering for the Klein-Gordon equations with time-dependent potentials ⋮ Energy decay estimates for the dissipative wave equation with space-time dependent potential ⋮ Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients ⋮ Weighted energy estimates for wave equations in exterior domains ⋮ Resolvent Estimates and Scattering Problems for Schrödinger, Klein-Gordon and Wave Equations ⋮ Asymptotic behaviour of solutions for the wave equation with an effective dissipation around the boundary ⋮ Energy decay of solutions to the wave equations with linear dissipation localized near infinity ⋮ Low and high energy resolvent estimates for wave propagation in stratified media and their applications. ⋮ Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients ⋮ Resolvent estimates and scattering states for dissipative systems.

Cites Work

• Unnamed Item
• Exponential decay for the semilinear wave equation with localized damping in unbounded domains
• Decaying states of perturbed wave equations
• Scattering theory for wave equations with dissipative terms
• Energy decay of solutions of dissipative wave equations
• On energy decay-nondecay problems for wave equations with nonlinear dissipative term in \(\mathbb{R}^ N\)

This page was built for publication: Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation