On perturbed wave equations with time-dependent coefficients
Gustavo Perla Menzala (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Gustavo Perla Menzala (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Vesselin M. Petkov, Vladimir S. Georgiev (1989)
Annales de l'I.H.P. Physique théorique
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Changxing Miao, Youbin Zhu (2006)
Colloquium Mathematicae
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We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for...
В.В. Залипаев, М.М. Попов (1991)
Zapiski naucnych seminarov Leningradskogo
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A. G. Ramm (2007)
Annales Polonici Mathematici
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It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.
J. C. Le Guillou, J. L. Basdevant (1972)
Annales de l'I.H.P. Physique théorique
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Mustapha Mokhtar-Kharroubi, Mohamed Chabi, Plamen Stefanov (1997)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Makoto Nakamura, Tohru Ozawa (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space with order . The assumptions on the nonlinearities are described in terms of power behavior at zero and at infinity such as for NLS and NLKG, and for NLW.