We consider the decay rate of solutions to nonlinear Klein-Gordon systems with a critical type nonlinearity. We will specify the optimal decay rate for a specific class of Klein-Gordon systems containing the dissipative nonlinearities. It will turn out that the decay rate which is previously found in some models is optimal.
Satoshi Masaki. Koki Sugiyama. "Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type." Differential Integral Equations 33 (5/6) 247 - 256, May/June 2020. https://doi.org/10.57262/die/1589594452