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Topic: Solution of Non-Linear PDE
Replies: 3   Last Post: May 30, 2013 12:42 PM

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 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
Re: Solution of Non-Linear PDE
Posted: May 30, 2013 12:42 PM

clicliclic@freenet.de schrieb:
>
> renatovitale77@gmail.com schrieb:

> >
> > Dear Ronald, please can you solve this:
> > du/dt + u du/dx = - m d^4x/dx^4 - i n d^2x/dx^2
> > with IC u(x,0) = sin (x).
> > x = [ 0 , 2pi ]; m and n are coefficients << 1 ; i is the imaginary unit.
> >
> > For n = m = 0 , this is the simply Burgers equation not viscous, but in this particulary case, I don't know how solve!
> >
> > Please, I have 3 questions:
> >
> > 1) Someone can solve this Burgers equation?
> > 2) What happens in the case of m << n ?
> > 3) What happens in the case of n << m ?
> >
> > Thanks

>
> Who's Ronald? Anyway, d^4x/dx^4 = 0 and d^2x/dx^2 = 0, no doubt. You
> probably mean d^4u/dx^4 and d^2u/dx^2, don't you?
>

The lack of response made me look into the reference:

<4usnp2\$jq6@usenetw1.news.prodigy.com>

This points to an August 14, 1996 (!) post by Ronald H. Brady starting a
thread "Solution of Non-Linear PDE". He announces a solution of du/dt +
u du/dx = 0 by means of series expansion.

<http://mathforum.org/kb/message.jspa?messageID=28465>

Martin.

Date Subject Author
5/29/13 renatovitale77@gmail.com
5/29/13 clicliclic@freenet.de
5/30/13 clicliclic@freenet.de