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Journal Article

Linear and nonlinear tails I: general results and perturbation theory

MPS-Authors

Szpak,  Nikodem
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

JoHDE05-741.pdf
(Publisher version), 331KB

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Citation

Szpak, N. (2008). Linear and nonlinear tails I: general results and perturbation theory. Journal of Hyperbolic Differential Equations, 5(4), 741-765. doi:10.1142/S0219891608001684.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-1491-4
Abstract
For nonlinear wave equations with a potential term, we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method which reduces the wave equation to an algebraic one. We demonstrate that already first and second perturbation orders, satisfying linear equations, can provide precise information about the decay of the full solution to the nonlinear wave equation.