On the decay estimate for small solutions to nonlinear Klein-Gordon equations with dissipative structure

Abstract

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.

arXiv comment17 pages

References in corpus (4)

• On Schrödinger systems with cubic dissipative nonlinearities of derivative type
• Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
• Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schrödinger equations
• On the derivative nonlinear Schrödinger equation with weakly dissipative structure