DECAY AND ASYMPTOTICS FOR THE ONE-DIMENSIONAL KLEIN-GORDON EQUATION WITH VARIABLE COEFFICIENT CUBIC NONLINEARITIES Academic Article uri icon

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.

published proceedings

  • SIAM JOURNAL ON MATHEMATICAL ANALYSIS

author list (cited authors)

  • Lindblad, H., Luhrmann, J., & Soffer, A.

citation count

  • 11

complete list of authors

  • Lindblad, Hans||Luhrmann, Jonas||Soffer, Avy

publication date

  • January 1, 2020 11:11 AM