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Math Help - Implicit solution of a PDE

  1. #1
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    Implicit solution of a PDE

    Hi! Can somebody help me with this exercise?
    Let F: \mathbb{R} \rightarrow \mathbb{R}^n, \, g: \mathbb{R}^n \rightarrow \mathbb{R} be smooth. Consider the following IVP on \mathbb{R}^n \times (0, \infty):

    u_t+F'(u) \cdot Du=0
    u(x,0)=g(x)

    Under which condition on F and g does u(x,t)=g(x-tF'(u(x,t))) define an implicit solution? When does this condition fail?

    I am pretty aimless and would be thankful for any ideas.
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  2. #2
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    I think it is just about calculating the derivatives but i do not get on here...
    Last edited by mr fantastic; January 17th 2009 at 05:26 PM. Reason: Removed the obvious bumping
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