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Classification of PDE

  1. Nov 12, 2011 #1
    Suppose you have a PDE with an arbitrary number of independent variables (not necessarily two), and of order n. Is there a nice classification akin to the hyperbolic, parabolic, etc.

    Thanks
     
  2. jcsd
  3. Nov 13, 2011 #2

    hunt_mat

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    There is, it's to do with the Monge cone (I think). I also am informed that there are equations which have no classification.
     
  4. Nov 13, 2011 #3
    This surprises me. Is this because forming a general classification system its more complicated than I imagine, or just that doing so serves little to no purpose?
     
  5. Nov 13, 2011 #4

    hunt_mat

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    It depends if you're saying is there a classification system for second order PDEs in n variables or if there is a classification system for PDEs with order n derivatives.
     
  6. Nov 13, 2011 #5
    Either really... Second order with n variables, or n order with 2 variables (or n order with m variables).
     
  7. Nov 13, 2011 #6

    hunt_mat

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    For second order equations in n variables, then it's to do with the Monge cone, with the other case I am not too sure as I am not an expert in this topic.
     
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