  In this case the answer to the first question is yes and to the second is no: there are no constraints on the data which can be put on S, but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from S as required by the initial data. If a line hits L− from the bottom, just continue it coming out of the top of L+ in the appropriate place, and if a line hits L+ from the bottom, continue it emerging from L− at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left: