Olimpiad problem

  • #1

Main Question or Discussion Point

I am having problems on this "said to be easy" olimpiad problem.
If anyone can give me some hints, I'd be greatful!
(unfortunately I could not get the subscripts to work, that is why everything that is superscribed should be lowered)
u[tex]_{tt}[/tex] = a(x)*u[tex]_{xx}[/tex]. x[tex]\in R[/tex]

a(x) = 1 (if x>0)
a(x) = 2 (if x<=0)

u|[tex]_{t=0}[/tex] = b(x) u[tex]_{t}[/tex]|[tex]_{t = 0}[/tex] = 0

b(x)= 0 when x[tex]\notin[/tex] [0, 1]
b(x) = 2x-2 when x[tex]\in [1, 1.5][/tex]
b(x) = -2x+4 when x[tex]\in[1.5, 2][/tex]

The problem is to draw the graph of the function u(t, x) when t = 5.

Answers and Replies

  • #2
I think that generalized functions have to be used here, although I am not 100% sure..
  • #3
Science Advisor
Whats U^tt. Is that supposed to be a double time derivative?
  • #4
yes, the indexes need to be a the bottom
  • #5
The thing is that I can solve the problem for any of the intervals ((-inf, 1), (1, 1.5), (1.5, inf)). But don't know how to get the general solution