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arXiv · 1907.09922

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

Hans Lindblad·Jonas Luhrmann·Avy Soffer
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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.

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Hans Lindblad, Jonas Luhrmann, Avy Soffer. 2019-07-23. Decay and asymptotics for the 1D Klein-Gordon equation with variable coefficient cubic nonlinearities. https://arxiv.org/abs/1907.09922

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