Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients

DOI10.1016/j.jde.2009.03.020zbMath1173.35032OpenAlexW2035286570MaRDI QIDQ1022936

Borislav Yordanov, Grozdena Todorova

Publication date: 10 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.03.020

zbMATH Keywords

weak dissipationmultiplier methodexponential decay ratepolynomial decay rate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (49)

Weighted \(L^2\)-estimates of solutions for damped wave equations with variable coefficients ⋮ Global existence and blow-up for semilinear wave equations with variable coefficients ⋮ Lifespan of solutions to the damped wave equation with a critical nonlinearity ⋮ Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain ⋮ The Generalized Diffusion Phenomenon and Applications ⋮ Energy decay in a wave guide with dissipation at infinity ⋮ Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients ⋮ Energy decay rate of the wave equations on Riemannian manifolds with critical potential ⋮ The Cauchy problem for the nonlinear damped wave equation with slowly decaying data ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term ⋮ Decay estimates for a kind of linear wave equations ⋮ General energy decay for wave equation with space-time potential and time delay in \(\mathbb{R}^n\) ⋮ Asymptotic expansion of solutions to the wave equation with space-dependent damping ⋮ Lifespan estimates for semilinear wave equations with space dependent damping and potential ⋮ Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in \({\mathbb {R}}^n\): (II) Overdamping Case ⋮ Asymptotic behavior for wave equations with space-dependent damping in a weighted energy class ⋮ Decay property of solutions to the wave equation with space‐dependent damping, absorbing nonlinearity, and polynomially decaying data ⋮ Fast decay of solutions for wave equations with localized dissipation on noncompact Riemannian manifolds ⋮ Diffusion phenomenon in Hilbert spaces and applications ⋮ Optimal decay rate of the energy for wave equations with critical potential ⋮ Small data global existence for the semilinear wave equation with space-time dependent damping ⋮ Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation ⋮ Unnamed Item ⋮ Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term ⋮ Blow-up of solutions to the one-dimensional semilinear wave equation with damping depending on time and space variables ⋮ Critical exponent for the semilinear wave equations with a damping increasing in the far field ⋮ Higher order energy decay for damped wave equations with variable 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 ⋮ Decay estimates for wave equations with variable coefficients ⋮ Klein-Gordon equations with homogeneous time-dependent electric fields ⋮ Energy decay rates of elastic waves in unbounded domain with potential type of damping ⋮ The diffusion phenomenon for dissipative wave equations in metric measure spaces ⋮ Nonlinear dissipative wave equations with space-time dependent potential ⋮ On diffusion phenomena for the linear wave equation with space-dependent damping ⋮ Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term ⋮ The diffusion phenomenon for damped wave equations with space-time dependent coefficients ⋮ Well-posedness of a class of hyperbolic partial differential equations on the semi-axis ⋮ Energy decay estimates for the dissipative wave equation with space-time dependent potential ⋮ Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations ⋮ Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data ⋮ A note on the lifespan of solutions to the semilinear damped wave equation ⋮ Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain ⋮ Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping ⋮ On global smooth solutions of the 3D spherically symmetric Euler equations with time-dependent damping and physical vacuum ⋮ Blowup for semilinear wave equation with space-dependent damping and combined nonlinearities ⋮ Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients ⋮ Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn

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