Lp - Lq Decay Estimates for Wave Equations with Time-Dependent Coefficients

DOI10.2991/jnmp.2004.11.4.9zbMath1071.35093OpenAlexW2155839779MaRDI QIDQ4653191

Michael Reissig

Publication date: 7 March 2005

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2991/jnmp.2004.11.4.9

zbMATH Keywords

oscillations in the coefficientsmass and dissipation terms

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (25)

Smoothing estimates for non-dispersive equations ⋮ \(L^p-L^q\) estimates for wave equations with strong time-dependent oscillations ⋮ Energy estimates for the Cauchy problem of Klein-Gordon-type equations with non-effective and very fast oscillating time-dependent potential ⋮ Decay estimates for a Klein-Gordon model with time-periodic coefficients ⋮ Decay property of solutions for damped wave equations with space-time dependent damping term ⋮ Random attractors for stochastic time-dependent damped wave equation with critical exponents ⋮ General energy decay for wave equation with space-time potential and time delay in \(\mathbb{R}^n\) ⋮ Optimal decay rate of the energy for wave equations with critical potential ⋮ Unnamed Item ⋮ Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term ⋮ 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 a class of semilinear weakly hyperbolic equations ⋮ Decay estimates for wave equations with variable coefficients ⋮ Existence of solution for the \(n\)-dimension second order semilinear hyperbolic equations ⋮ Nonlinear dissipative wave equations with space-time dependent potential ⋮ Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term ⋮ Time decay for hyperbolic equations with homogeneous symbols ⋮ Energy decay estimates for the dissipative wave equation with space-time dependent potential ⋮ Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients ⋮ Generalised energy conservation law for wave equations with variable propagation speed ⋮ Asymptotic behaviors of solutions for time dependent damped wave equations ⋮ Advection versus diffusion in Richtmyer-Meshkov mixing ⋮ \(L^{2}\)-estimates of solutions for damped wave equations with space-time dependent damping term ⋮ Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients

Cites Work

• Unnamed Item
• On the asymptotic behavior of solutions of semi-linear wave equations
• About the solvability behaviour for special classes of nonlinear hyperbolic equations
• A priori estimates for the wave equation and some applications
• \(L^ p\)-decay rates for homogeneous wave-equations
• Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation
• One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations
• L p − L q Decay Estimates for the Wave Equations with Exponentially Growing Speed of Propagation
• Solution representations for a wave equation with weak dissipation
• Fourier transforms of surface-carried measures and differentiability of surface averages
• Parameteric resonance and nonexistence of the global solution to nonlinear wave equations

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