Displaying similar documents to “Decay of solutions of the wave equation in the exterior of several convex bodies”

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...

Invisible obstacles

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.

Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations

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 ℝ n with order s < n / 2 . The assumptions on the nonlinearities are described in terms of power behavior p 1 at zero and p 2 at infinity such as 1 + 4 / n ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLS and NLKG, and 1 + 4 / ( n - 1 ) ≤ p 1 ≤ p 2 ≤ 1 + 4 / ( n - 2 s ) for NLW.