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How to find uniqueness in first order pde

  1. Mar 21, 2009 #1
    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?
     
  2. jcsd
  3. Mar 22, 2009 #2

    HallsofIvy

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    You know it is unique if the conditions for the "existance and uniqueness" theorem hold. What are those conditions?
     
  4. Mar 22, 2009 #3
    Ah ok. Thanks
     
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