On the initial-value problem in a cold plasma model

We consider a homogeneous, weakly ionized gas filling all of space and in it the propagation of a plane electromagnetic wave induced at positive times by the electromagnetic field story at negative times and by an assigned external current. The propagation can be described by an integro-differential equation if one takes into account the collisions between molecules and electrons by a suitable linear inheritance relation. We determine explicitly the fundamental solution and therefore solve the associated classical initial value problem with completely arbitrary initial data.