Decay of solutions of the wave equation in the exterior of several convex bodies

Mitsuru Ikawa

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

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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RAGE theorem for power bounded operators and decay of local energy for moving obstacles

Vesselin M. Petkov, Vladimir S. Georgiev (1989)

Annales de l'I.H.P. Physique théorique

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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...

Коротковолновое скользящее рассеяние плоской волны на гладкой периодической границе. II. Дифракция на бесконечной периодической границе

В.В. Залипаев, М.М. Попов (1991)

Zapiski naucnych seminarov Leningradskogo

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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.

Crossing and experimental ππ S and P waves

J. C. Le Guillou, J. L. Basdevant (1972)

Annales de l'I.H.P. Physique théorique

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Scattering theory with two $L^{1}$ spaces : application to transport equations with obstacles

Mustapha Mokhtar-Kharroubi, Mohamed Chabi, Plamen Stefanov (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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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 $1 + 4 / n \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLS and NLKG, and $1 + 4 / (n - 1) \leq p_{1} \leq p_{2} \leq 1 + 4 / (n - 2 s)$ for NLW.