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Paper detail

Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities

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.

preprint2020arXivOpen access
Hans LindbladJonas LuhrmannAvy Soffer
math.APmath-phmath.MP
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Hans LindbladJonas LuhrmannAvy Soffer

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