Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities
Analysis of PDEs
2020-09-22 v2 Mathematical Physics
math.MP
Abstract
We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to deal with the long-range nature of the cubic nonlinearity become problematic in the presence of variable coefficients. We introduce a novel approach based on pointwise-in-time local decay estimates for the Klein-Gordon propagator to overcome this impasse.
Cite
@article{arxiv.1907.09922,
title = {Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities},
author = {Hans Lindblad and Jonas Luhrmann and Avy Soffer},
journal= {arXiv preprint arXiv:1907.09922},
year = {2020}
}
Comments
27 pages. Minor revisions. To appear in SIAM J. Math. Anal