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Math Help - 2nd Order Linear PDE Canonical Form Query

  1. #1
    Senior Member bugatti79's Avatar
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    2nd Order Linear PDE Canonical Form Query

    Folks,

    I am trying to see a pattern when solving 2nd order linear PDE's.

    The canonical form for the Hyperbolic case is

    \bar B w_{st}+ \phi(w_s,w_t,s,t,w)=0 where \bar B \ne0

    If the discriminant is a real number does the \phi term vanish and hence if the discriminant is some f(x,y)>0, do we always have some \phi terms?

    And similarly for the elliptical case?

    Thanks
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  2. #2
    MHF Contributor
    Jester's Avatar
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    Re: 2nd Order Linear PDE Canonical Form Query

    Generally speaking there will be lower order terms. Sometimes (if you're lucky) you can integrate your transformed PDE once or even twice.
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