Scattering theory for wave equations with dissipative terms
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Publication:1238095
DOI10.2977/prims/1195190721zbMath0357.35067OpenAlexW2027285046MaRDI QIDQ1238095
Publication date: 1976
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/1195190721
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Wave equations with time-dependent dissipation. I: Non-effective dissipation ⋮ Exponential decay and spectral structure for wave equation with some dissipations ⋮ Asymptotic completeness in dissipative scattering theory ⋮ Remarks on the asymptotic behavior of the solution to damped wave equations ⋮ Smooth Spectral Calculus ⋮ Diffusion phenomena for the wave equation with space-dependent damping in an exterior domain ⋮ Energy decay in a wave guide with dissipation at infinity ⋮ 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 ⋮ Energy decay rate of the wave equations on Riemannian manifolds with critical potential ⋮ Asymptotic profile of solution for the Cauchy problem of beam equation with variable coefficient ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ Decay estimates for a kind of linear wave equations ⋮ General energy decay for wave equation with space-time potential and time delay in \(\mathbb{R}^n\) ⋮ Critical exponent for nonlinear damped wave equations with non-negative potential in 3D ⋮ Asymptotic expansion of solutions to the wave equation with space-dependent damping ⋮ Lifespan estimates for semilinear wave equations with space dependent damping and potential ⋮ 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 ⋮ 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 ⋮ Inverse scattering for the stationary wave equation with a friction term in two dimensions ⋮ Small data global existence for the semilinear wave equation with space-time dependent damping ⋮ 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 ⋮ Divergence-type Operators: Spectral Theory and Spacetime Estimates ⋮ 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 ⋮ Scattering theory for Lindblad master equations ⋮ Stability for second order abstract evolution equations ⋮ 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 ⋮ Decay Properties for the Damped Wave Equation with Space Dependent Potential and Absorbed Semilinear Term ⋮ EIGENFUNCTION EXPANSIONS AND SPACETIME ESTIMATES FOR GENERATORS IN DIVERGENCE-FORM ⋮ Energy decay of solutions of dissipative wave equations ⋮ Weighted \(L^2\)-estimates for dissipative wave equations with variable coefficients ⋮ Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data ⋮ Asymptotic behavior of solutions to the semilinear wave equation with time-dependent damping ⋮ Remark on the blow-up of solutions for the semilinear wave equation with overdamping term ⋮ Weighted energy estimates for wave equations in exterior domains ⋮ Energy decay and asymptotic behavior of solutions to the wave equations with linear dissipation ⋮ Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain ⋮ 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. ⋮ Diffusion phenomenon for abstract linear wave equations with time decaying coefficients of propagation and dissipation ⋮ Decay of energy for wave equations with strong damping terms and space–time-dependent coefficients ⋮ Resolvent estimates and scattering states for dissipative systems.
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