Folks,

I am struggling to get the initial conditions @ t=0 for p and q.

Given for on

My attempt:

Parameterise x such that and and differentiate the given IC

This gives

Not sure if this right or how to proceed further to find pand q?

Thanks

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- August 14th 2011, 07:50 AMbugatti79Charpits: Non Linear 1st order PDE: Particular IC
Folks,

I am struggling to get the initial conditions @ t=0 for p and q.

Given for on

My attempt:

Parameterise x such that and and differentiate the given IC

This gives

Not sure if this right or how to proceed further to find pand q?

Thanks - August 15th 2011, 06:49 AMJesterRe: Charpits: Non Linear 1st order PDE: Particular IC
So now you have one equation

.

Your second equation is the PDE itself .

Two equations for two unknowns. Now solve for and .

BTW - what do you mean @ . There's no in this problem.

Because of the symmetry of the BC, I might also suggest switching to polar coordinates. - August 15th 2011, 10:40 AMbugatti79Re: Charpits: Non Linear 1st order PDE: Particular IC
- August 15th 2011, 11:18 AMbugatti79Re: Charpits: Non Linear 1st order PDE: Particular IC
Maybe I should clarify that in this problem we have u=0 when x^2+y^2=1. These are the IC's I take at t=0. I hope that makes sense. This is the approach I take for all other charpit problems based on my notes.

- August 15th 2011, 12:16 PMJesterRe: Charpits: Non Linear 1st order PDE: Particular IC
I'm good. I usually use and and leave for a time variable :-)

- August 15th 2011, 12:21 PMbugatti79Re: Charpits: Non Linear 1st order PDE: Particular IC
- August 15th 2011, 01:18 PMJesterRe: Charpits: Non Linear 1st order PDE: Particular IC
Actually you can! If for all and then certainly along some curve (as long as the derivatives exist).

- August 15th 2011, 01:38 PMbugatti79Re: Charpits: Non Linear 1st order PDE: Particular IC
- August 22nd 2011, 12:59 PMbugatti79Re: Charpits: Non Linear 1st order PDE: Particular IC
- August 22nd 2011, 01:47 PMJesterRe: Charpits: Non Linear 1st order PDE: Particular IC
Looks good be I might be careful on the .