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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?

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# How to find uniqueness in first order pde

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