Asymptotic behaviour for semilinear damped wave equations on ${\mathbb {R}}^N$

Feireisl, Eduard

Displaying similar documents to “Asymptotic behaviour for semilinear damped wave equations on $ℝ^{N}$ ”

Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

Petronela Radu (2008)

Applicationes Mathematicae

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We show local existence of solutions to the initial boundary value problem corresponding to a semilinear wave equation with interior damping and source terms. The difficulty in dealing with these two competitive forces comes from the fact that the source term is not a locally Lipschitz function from H¹(Ω) into L²(Ω) as typically assumed in the literature. The strategy behind the proof is based on the physics of the problem, so it does not use the damping present in the equation. The...

Blowup of solutions of a nonlinear wave equation.

Benaissa, Abbes, Messaoudi, Salim A. (2002)

Journal of Applied Mathematics

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Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms

Mohammed Aassila (1999)

Commentationes Mathematicae Universitatis Carolinae

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In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.

Existence of Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. (1996)

Serdica Mathematical Journal

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∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology. In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was...

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

Yue Liu, Masahito Ohta, Grozdena Todorova (2007)

Annales de l'I.H.P. Analyse non linéaire

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The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

Jonathan Luk (2013)

Journal of the European Mathematical Society

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We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region ${r \leq \frac{t}{4}}$ .

On the energy critical focusing non-linear wave equation

Carlos E. Kenig, Frank Merle (2006-2007)

Séminaire Équations aux dérivées partielles

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Displaying similar documents to “Asymptotic behaviour for semilinear damped wave equations on ℝ N ”

Weak solutions to the initial boundary value problem for a semilinear wave equation with damping and source terms

Blowup of solutions of a nonlinear wave equation.

Uniform stabilization of solutions to a quasilinear wave equation with damping and source terms

Existence of Global Solutions to Supercritical Semilinear Wave Equations

Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations

The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

On the energy critical focusing non-linear wave equation

Displaying similar documents to “Asymptotic behaviour for semilinear damped wave equations on $ℝ^{N}$ ”