Weakly coupled systems of semi-linear Klein-Gordon equations with memory-type dissipation

Abstract

We are concerned with the existence of global in time solutions to the Cauchy problem for semi-linear Klein-Gordon equations with memory-type dissipation in ${\mathbb{R}}^n$. In the first place, we consider the linearized equation: applying the energy method in the Fourier space, we derive the point-wise estimate of a solution in the Fourier space. However, we found that the function in energy estimates has a mistake.

arXiv commentThe function in energy estimates has a mistake.