Semi Linear PDE Sample Question

• Aug 3rd 2011, 10:00 PM
bugatti79
Semi Linear PDE Sample Question
Hi Folks,

Looking a sample exam question...

(i) Write down the general form of a semi linear first order PDE in u(x,y)

$a(x,y) \frac{\partial u}{\partial x} +b(x,y) \frac{\partial u}{\partial y}=h(x,y,u)$

(ii) Write down the ordinary differential equation satisfied by a characteristic curve in the xy plane for your pde in (i)

$\frac{dy}{dx}=\frac{b(x,y)}{a(x,y}$ and $a(x,y) \ne 0$

(iii)Give a careful consideration of the ordinary differential equation satisfied by u(x,y) along such a characteristic curve?

I have not found anything in my notes regarding this...May anyone help?

Thanks
• Aug 4th 2011, 05:08 AM
Jester
Re: Semi Linear PDE Sample Question
Is what you have written exactly the way the question was written because it looks like to me that you already have answers to part (i) and (ii).
• Aug 4th 2011, 05:38 AM
bugatti79
Re: Semi Linear PDE Sample Question
Quote:

Originally Posted by Danny
Is what you have written exactly the way the question was written because it looks like to me that you already have answers to part (i) and (ii).

Hi Danny,

Sorry Danny for lack of clarity. The math I have written is my attempt at parts i and ii.

I do not know iii.....?

Thanks