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

Changxing Miao, and Youbin Zhu. "Scattering theory for a nonlinear system of wave equations with critical growth." Colloquium Mathematicae 106.1 (2006): 69-81. <http://eudml.org/doc/284007>.

@article{ChangxingMiao2006,
abstract = { 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 the potential energy. The resulting global-in-time estimates imply immediately the existence of the wave operators and the scattering operator. },
author = {Changxing Miao, Youbin Zhu},
journal = {Colloquium Mathematicae},
keywords = {Strichartz estimate; wave operator; scattering operator; decay estimate},
language = {eng},
number = {1},
pages = {69-81},
title = {Scattering theory for a nonlinear system of wave equations with critical growth},
url = {http://eudml.org/doc/284007},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Changxing Miao
AU - Youbin Zhu
TI - Scattering theory for a nonlinear system of wave equations with critical growth
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 1
SP - 69
EP - 81
AB - 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 the potential energy. The resulting global-in-time estimates imply immediately the existence of the wave operators and the scattering operator.
LA - eng
KW - Strichartz estimate; wave operator; scattering operator; decay estimate
UR - http://eudml.org/doc/284007
ER -