DECAY AND ASYMPTOTICS FOR THE ONE-DIMENSIONAL KLEIN-GORDON EQUATION WITH VARIABLE COEFFICIENT CUBIC NONLINEARITIES
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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.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
author list (cited authors)
Lindblad, H., Luhrmann, J., & Soffer, A.
complete list of authors
Lindblad, Hans||Luhrmann, Jonas||Soffer, Avy