Solving PDE for F and F' in 2D Space: Relation between Variables x, t and t

[Arjun S]

If I have a function "F" in a two-dimensional space F(x,t) and its analog F' in another co-ordinate system F'(x',t') and the relation between the two is given by :

∂F/∂t −c(∂F/∂x) =∂F ′/ ∂t ′

How do I find a relation between F and F ′ and between the variables x,t and t ′ ?

 

[MathematicalPhysicist]

If you also had:

∂F'/∂t' −c(∂F'/∂x') =∂F / ∂t

Then you'll get: F'_x' = -F_x.
But you still need another constraint to find a relation between F and F'.

The problem as it is stated doesn't seem to me solvable, perhaps someone else knows better than me.