Displaying similar documents to “Time Decay for Nonlinear Wave Equations in Two Space Dimensions.”

On the nonlinear stabilization of the wave equation

Aissa Guesmia (1998)

Annales Polonici Mathematici

Similarity:

We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.

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

Changxing Miao, Youbin Zhu (2006)

Colloquium Mathematicae

Similarity:

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...

Scattering of small solutions of a symmetric regularized-long-wave equation

Sevdzhan Hakkaev (2004)

Applicationes Mathematicae

Similarity:

We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.