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Non-canonical form into canonical transformation 1-d partial dif.

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems
    with non-canonical boundary conditions to the canonical ones and write down the
    equations in terms of the variable ˜u (do not solve them). Note that there are
    infinitely many u1’s that solve each problem—try to find the simplest ones.
    (a) Heat equation
    ut = Uxx , x ∈ [0, l] ,
    with the following boundary conditions
    (a.1) u(0, t) = U(l, t) = A ,
    (a.2) Ux(0, t) = 0 , U(l, t) = A ,
    (a.3) U(0, t) = A , U(l, t) = B ,
    (a.4) Ux(0, t) = Ux(l, t) = A ,
    (a.5) Ux(0, t) = A , Ux(l, t) = B .
    (b) Wave equation with dissipation and a perturbation on one end
    Utt + aUt = c
    2Uxx , x ∈ [0, l]

    2. Relevant equations


    3. The attempt at a solution
    I am using
    U1(x,t)= a(t)+(x-c).b(t)

    then U(x,t)=U(tilda)(x,t)+U1(x,t)

    I can find the U1's but not U(tilda)
    is that enough to transform them into canonical form?
    I'm googling like a mad man but no luck so far. can't find any good sources.
    you don't have to answer the question but a little help would be nice.
     
  2. jcsd
  3. Oct 11, 2014 #2
    Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Oct 11, 2014 #3
    I've found the correct method.
    Thanks anyway.
     
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