We consider the Cauchy problem for cubic nonlinear Klein-Gordon equations in one space dimension. We give the $L^p$-decay estimate for the small data solution and show that it decays faster than the free solution if the cubic nonlinearity has the suitable dissipative structure.
A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension
Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities
Life span of small solutions to a system of wave equations
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