How to find uniqueness in first order pde

[somethingstra]

Hi guys,

I have a general problem that I'm not quite sure how to solve. Suppose you have a first order pde, like Ut=Ux together with some boundary conditions.

You'd do the appropriate transformations that lead to a solution plus an arbitrary function defined implicitly. How would you know that the solution is unique? Is there anyway to work with the initial conditions to figure that out?

 

[HallsofIvy]

You know it is unique if the conditions for the "existance and uniqueness" theorem hold. What are those conditions?

 

[somethingstra]

Ah ok. Thanks