Understand
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.
- In a forthcoming publication (part II) we address the issue of optimal decay estimates and precise asymptotics under spherical symmetry where the perturbation equations can be solved almost exactly.
Built on
Analytic function theory
E. Hille · 1962
Earlier work this paper cites.
Asakura F · 1986
Earlier work this paper cites.
Similar
Existence and blow up of small amplitude nonlinear waves with a negative potential
W. Strauss and K. Tsutaya · 1997
Cited alongside, same era.
Weighted- L ∞ {L}^{\infty} and pointwise space-time decay estimates for wave equations with potentials and initial data of low regularity
N. Szpak · 2007
Cited alongside, same era.
Then
Linear and nonlinear tails II: spherical symmetry
N. Szpak, P. Bizon, T. Chmaj, and A. Rostworowski · 2007
Closest in time.
Simple proof of a useful pointwise estimate for the wave equation
N. Szpak · 2007
Closest in time.
Beyond the bibliography
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…