Punktförmige Zugbeeinflussung
After acknowledging the warning signal the train has to stay below the braking curve (German "Bremskurve") - fast trains may travel up to 165 km/h and they must reduce the speed to below 85 km/h after 23 seconds. Note that the operation of high speed trains beyond 165 km/h is not based on visual wayside signals or PZB inductors (using LZB or European Train Control System cab-signalling instead in Germany).
Eurostar
The trains are essentially modified TGV sets, and can operate at up to on high-speed lines, and in the Channel Tunnel. It is possible to exceed the 300-kilometre-per-hour speed limit, but only with special permission from the safety authorities in the respective country.
Speed limits in the Channel Tunnel are dictated by air-resistance, energy (heat) dissipation and the need to fit in with other, slower trains. The trains were designed with Channel Tunnel safety in mind, and consist of two independent "half-sets" each with its own power car. In the event of a serious fire on board while travelling through the tunnel, passengers would be transferred into the undamaged half of the train, which would then be detached and driven out of the tunnel to safety.
If the undamaged part were the rear half of the train, this would be driven by the Chef du Train, who is a fully authorised driver and occupies the rear driving cab while the train travels through the tunnel for this purpose.