Energy estimates for wave equations with time dependent propagation speeds in the Gevrey class
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Publication:979029
DOI10.1016/J.JDE.2010.03.003zbMath1198.35032OpenAlexW1986801629MaRDI QIDQ979029
Publication date: 25 June 2010
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2010.03.003
Asymptotic behavior of solutions to PDEs (35B40) Wave equation (35L05) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)
Related Items (7)
\( \sigma \)-evolution models with low regular time-dependent effective structural damping ⋮ Response solutions for wave equations with variable wave speed and periodic forcing ⋮ On second order weakly hyperbolic equations and the ultradifferentiable classes ⋮ Generalized energy conservation for Klein-Gordon type equations ⋮ Blow-up of the energy at infinity for 2 by 2 systems ⋮ Influence of strong time-dependent oscillations in semilinear damped wave models ⋮ On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions
Cites Work
- \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
- Loss of regularity for second order hyperbolic equations with singular coefficients
- Global solvability for Kirchhoff equation in special classes of non-analytic functions
- Unique existence of evolution equations of hyperbolic type with countably many singular or degenerate points
- On the global solvability of Kirchhoff equation for non-analytic initial data
- On the asymptotic behavior of the energy for the wave equations with time depending coefficients
- Direct proof of the perfect block diagonalization of systems of pseudo-differential operators in the ultradifferentiable classes
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