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Olimpiad problem

  1. Apr 9, 2008 #1
    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.
     
  2. jcsd
  3. Apr 9, 2008 #2
    I think that generalized functions have to be used here, although I am not 100% sure..
     
  4. Apr 9, 2008 #3

    Haelfix

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    Science Advisor

    Whats U^tt. Is that supposed to be a double time derivative?
     
  5. Apr 10, 2008 #4
    yes, the indexes need to be a the bottom
     
  6. Apr 11, 2008 #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
     
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