Displaying similar documents to “Scattering theory with two L 1 spaces : application to transport equations with obstacles”

Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity

Demontis, Francesco, der Mee, Cornelis van (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10. In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.

Scattering theory for a nonlinear system of wave equations with critical growth

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...

Asymptotic behaviour of the scattering phase for non-trapping obstacles

Veselin Petkov, Georgi Popov (1982)

Annales de l'institut Fourier

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Let S ( λ ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪 ⊂ R n , n ≥ 3 with Dirichlet or Neumann boundary conditions on ∂ 𝒪 . The function s ( λ ) , called scattering phase, is determined from the equality e - 2 π i s ( λ ) = det S ( λ ) . We show that s ( λ ) has an asymptotic expansion s ( λ ) ∼ ∑ j = 0 ∞ c j λ n - j as λ → + ∞ and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

Scattering problems in a domain with small holes.

V. Chiadò Piat, M. Codegone (2003)

RACSAM

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In this paper, we consider a family of scattering problems in perforated unbounded domains Ω. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.

Scattering Matrix for the Reflection-Transmission Problem in a Viscoelastic Medium

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. ...