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

• Autorzy: Changxing Miao , Youbin Zhu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35L15: Initial value problems for second-order hyperbolic equations
• 35L05: Wave equation
• 35P25: Scattering theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 1
• Strony: 69-81

Daty

wydano

2006

Twórcy

autor

Changxing Miao

• Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

autor

Youbin Zhu

• Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China

Identyfikatory

DOI

10.4064/cm106-1-6