On the radius of spatial analyticity for the 1d Dirac-Klein-Gordon equations

We study the well-posedness of the Dirac-Klein-Gordon system in one space dimension with initial data that have an analytic extension to a strip around the real axis. It is proved that the radius of analyticity of the solutions at time $t$ cannot decay faster than $1\mathrm{/}{t}^4$ as $t$ tends to infinity.