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 $1/t^4$ as $t$ tends to infinity. 
Sigmund Selberg and Achenef Tesfahun
math.AP