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Request for Hints to solve a Non-Linear PDE

  1. Oct 7, 2012 #1
    Dear Friends,
    Would you please provide me with some hints to find the analytical solution of the non-linear PDE given below:
    U=U(z,t)

    Uzz-(A/U)*Uz=Ut

    BC's and IC's are:
    U(z,0)=B
    U(1,t)=B
    Uz(0,t)=A*H(t); "H" is the heaviside function and H(0)=0

    where A, B, and C are constant.


    Many Thanks,
     
  2. jcsd
  3. Oct 9, 2012 #2
    Hi !

    Since there is no answer yet to the question, I dare give my opinion on the subject.
    The analytical solutions of most of the non-linear PDE are not known. The solutions of only a few of them can be formally expressed (generally in case of school problems). In practice, numerical methods are used to treat the problems involving PDE in physics or industry.
    I think that the mohammad449's non-linear PDE should be treated with a numerical software.
    Nevertheless, I hope that someone will give a more theoretical answer.
     
  4. Oct 9, 2012 #3
    Thanks so much Dear JJacquelin!

    Actually, the original equation has been simplified to the given form. I have the numerical results of the original complicated equation.
    Currently, I am trying to find an analytical solution to match the numerical one. I tried the Heat Integral method (to get an approximation) but the resulting solution was not accurate enough, it just works in some specific conditions.
     
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