Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities

Abstract

We consider the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution gains an additional logarithmic decay in comparison with the free evolution in the sense of $L^p$, $2\le p\le \infty$.

17 pages

References in corpus (1)

• A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D