Existence of complete Lyapunov functions for semiflows on separable   metric spaces
  The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows on separable metric spaces. 
Mauro Patr\~ao
math.DS