Nonlinear scattering theory for a class of wave equations in \(H^{s}\)

DOI10.1016/j.jmaa.2004.03.050zbMath1060.35099OpenAlexW2054171507MaRDI QIDQ1876731

Bao Xiang Wang

Publication date: 20 August 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.03.050

zbMATH Keywords

semilinear wave equationnonlinear Schrödinger equationspatial decaysemilinear Klein-Gordon equationnonlinear scattering operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (14)

On the blow-up of the Cauchy problem of higher-order nonlinear viscoelastic wave equation ⋮ Decay estimates for a class of wave equations ⋮ Non-integer power estimate in modulation spaces and its applications ⋮ Existence and nonexistence of global solutions for higher-order nonlinear viscoelastic equations ⋮ Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term ⋮ Global existence and asymptotic behaviour for systems of nonlinear hyperbolic equations ⋮ Self-similar solutions for nonlinear Schrödinger equations ⋮ Existence and asymptotic behavior of global solutions for a class of nonlinear higher-order wave equation ⋮ Existence and asymptotic behavior for systems of nonlinear hyperbolic equations ⋮ Solvability of the Cauchy problem of nonlinear beam equations in Besov spaces ⋮ Local well-posedness for the inhomogeneous nonlinear Schrödinger equation in \(H^s ( \mathbb{R}^n )\) ⋮ Energy scattering theory for the nonlinear Schrödinger equations with exponential growth in lower spatial dimensions ⋮ Small data global well-posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in \(H^s (\mathbb{R}^n)\) ⋮ Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term

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