renegade05
Full Member
- Joined
- Sep 10, 2010
- Messages
- 260
Hello there!
I am having problems with the following question:
\(\displaystyle x u_x+y u_y - 3u=0\)
With \(\displaystyle u(x,1)=\phi(x)\)
I solved it using method of characteristics to find the solution to be:
\(\displaystyle u(x,y) = \phi(\frac{x}{y}) y^3\)
With the data curve being \(\displaystyle y=1\) (red line)
And characteristic base curves being \(\displaystyle y=\frac{1}{\xi}x\) (black lines)
So plotting this with different values of \(\displaystyle \xi\) we get the following idea:
Now the question asks to:
"explain how the problem needs to be restricted in order to have a unique solution."
So this is where I am stuck. Everything looks good to me - so what am I missing? What are these restrictions?
THANKS!
I am having problems with the following question:
\(\displaystyle x u_x+y u_y - 3u=0\)
With \(\displaystyle u(x,1)=\phi(x)\)
I solved it using method of characteristics to find the solution to be:
\(\displaystyle u(x,y) = \phi(\frac{x}{y}) y^3\)
With the data curve being \(\displaystyle y=1\) (red line)
And characteristic base curves being \(\displaystyle y=\frac{1}{\xi}x\) (black lines)
So plotting this with different values of \(\displaystyle \xi\) we get the following idea:
Now the question asks to:
"explain how the problem needs to be restricted in order to have a unique solution."
So this is where I am stuck. Everything looks good to me - so what am I missing? What are these restrictions?
THANKS!