Solving PDEs with Shocks: Analyzing Solutions

[sara_math]

PDE + shock !

Ux + 2Uy = 0

I.C: U(x,y=2x) = exp(x)

solution:-
y=2x+c1
x=c2
using I.C
c1=0
c2=exp(x)

No solution since I.C on the characteristics line

every thing is ok until here but my teacher said that there exist one case that when u change some thing u will get a solution

how !




also i want 2 know why discont. or shock occur ?


i hope u can help me

 

[quantumdude]

every thing is ok until here but my teacher said that there exist one case that when u change some thing u will get a solution

how !

Can you be more specific? I'm not following you.

Also could you not use "chat room" slang? It took me a while to figure out that "u" means "you" and not the solution to the PDE. Thanks.

 

[sara_math]

Also could you not use "chat room" slang? <--- Sorry !

Can you be more specific? <--- ok

For the PDE there is no solution except one case, what is this case ?
the proffisor said you can change something to have that case

 

[dextercioby]

If I'm not mistaking, should the characteristics' eq be

[tex]x+2y=C [/itex] ...?<br /> <br /> Daniel.[/tex]

 

[sara_math]

ok ill try it then ill tell you the result

thnx