期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 52, 期 6, 页码 6379-6411出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1323722
关键词
Klein-Gordon equation; long-range scattering; variable coefficient nonlinearity; asymptotic stability of kink solutions
资金
- National Science Foundation [DMS-1600749, DMS-1500925]
- National Natural Science Foundation of China [11671163]
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.
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