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PDE solution uniqueness

  1. Jun 8, 2009 #1
    Hi All,

    I am dealing with the heat equation these days and in an attack of originality I thought I would find a new solution to it, namely

    (dT/dt)=d^2T/dx^2

    has a solution of the type

    T(x,t) = ax^2+2t

    Now, I do not know much about the existence and uniqueness of PDE solutions, but for some reason I though the existence of solution other than the one found by, e.g., variable sepration, was refused for this PDE. The Cauchy -Kowalewskaya theorem does not say much, it seems to me, until the boundary considtions are fixed.

    Does anybody has a clear grasp on the matter, for which I would be the most grateful?

    Many thanks

    Regards

    Muzialis
     
  2. jcsd
  3. Jun 8, 2009 #2

    Hootenanny

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    Uniqueness only applies to well posed problems. A PDE without boundary conditions is ill posed.

    For a given PDE without boundary conditions, there are either infinitely many solutions or no solutions.

    You should also note that in your case your solution is only a valid solution if a = 1.

    (Moving to the Mathematics forums)
     
  4. Jun 8, 2009 #3
    Hootenanny,

    thank you for your valuable reply.


    Best Regards

    Muzialis
     
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