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Math Help - Help with solving a second order non-linear pde

  1. #1
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    Help with solving a second order non-linear pde

    Hello!

    I have a second order non-linear partial differential equation. I've tried to solve it by using a transformation of variables, without success so far...

    It can be that my equation does not have an analytical solution, but i'm not sure. Can anyone help me please?

    I attached the equation in a pdf file. I'm sorry, i got a LATEX error trying to insert the equation into the post.

    Thank you very much!
    Attached Files Attached Files
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  2. #2
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    Re: Help with solving a second order non-linear pde

    The PDE is question is

    Dx^2f_{xx} + C x f_x + B\left(f_xf_y^{\beta}\right)^{\frac{1}{1-\beta}} + A f_x^{\frac{\alpha - 1}{\alpha}} = 0 .

    A few questions. Are A-D constant? Is \alpha and \beta constant? Are there are particular values of  \alpha and \beta that are of interest? What if \alpha = 0 or \beta = 1? Do you limiting PDEs for these?
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  3. #3
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    Re: Help with solving a second order non-linear pde

    Thank you very much for your reply,

    Actually, A-D are constants. Also \alpha and \beta are constants, and are expected to be less than zero.

    Thank you again!

    Alejandro
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