Some new results in spectral and scattering theory of differential operators on
S. Agmon (1978-1979)
Séminaire Équations aux dérivées partielles (Polytechnique)
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S. Agmon (1978-1979)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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...
Alessia Berti (2007)
Bollettino dell'Unione Matematica Italiana
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The reflection-transmission problem of time-harmonic waves in a viscoelastic, anisotropic and stratified solid is examined. The medium is supposed to occupy the whole space. The waves are sent either from upwards or downwards with oblique incidence. The scattering matrix is defined by generalizing the procedure followed in the scalar case, namely, when the solid is isotropic and the wave incidence is normal. Existence, uniqueness and properties of the scattering matrix are discussed. ...
Mustapha Mokhtar-Kharroubi, Mohamed Chabi, Plamen Stefanov (1997)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Roach, Gary F.
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Lars Hörmander (1976)
Mathematische Zeitschrift
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Mitsuru Ikawa (1985)
Journées équations aux dérivées partielles
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Sevdzhan Hakkaev (2004)
Applicationes Mathematicae
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We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.
White, Denis A.W. (1992)
International Journal of Mathematics and Mathematical Sciences
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