Optimal decay rate of solutions for nonlinear Klein-Gordon systems of critical type

TL;DR

This paper determines the optimal decay rate of solutions for a class of nonlinear Klein-Gordon systems with critical nonlinearities, including dissipative effects, confirming the previously known decay rates are indeed optimal.

Contribution

It establishes the precise optimal decay rate for a specific class of nonlinear Klein-Gordon systems with critical nonlinearities, including dissipative nonlinearities.

Findings

Decay rate previously found is optimal

Explicit decay rate for a class of Klein-Gordon systems

Includes systems with dissipative nonlinearities

Abstract

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 nonlinearites. It will turn out that the decay rate which is previously found in some models is optimal.