Help with solving a second order non-linear pde

**Amosino** · October 10th 2011, 06:19 AM

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!

**Danny** · October 10th 2011, 01:58 PM

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?

**Amosino** · October 11th 2011, 12:21 AM

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

Thread: Help with solving a second order non-linear pde

LinkBack

Thread Tools

Display

Help with solving a second order non-linear pde

Re: Help with solving a second order non-linear pde

Re: Help with solving a second order non-linear pde

Similar Math Help Forum Discussions

3rd-order to first order ODE and solving

Linear program with higher order non-linear constraints.

Solving 1st order non-linear differential Equation

Second order linear equations, reduction of order

2nd order homogenous in to 1st order linear systems

Search Tags