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Wave equation with nonhomogenous neumann BC

  1. Jul 2, 2012 #1
    I've been searching online for the past week but can't seem to find what im looking for.

    I need the analytic solution to the wave equation: utt - c^2*uxx = 0

    with neumann boundary conditions that are not homogeneous, i.e. ux(0,t) = A, for nonzero A.

    also, the domain i require the solution to be in is a bounded domain (0 to L) or better yet the semi-infinite domain (0 to ∞)

    can anyone refer me to a source?

    Thank you
  2. jcsd
  3. Jul 3, 2012 #2
    So it's utt - c2uxx = 0
    ([noparse]utt - c2uxx = 0[/noparse])

    The general solution is easy: u = u1(x - c*t) + u2(x + c*t)
    for arbitrary functions u1 and u2.
    One can find it by changing variables to w1 = x - c*t and w2 = x + c*t

    One can see from that solution that a single boundary condition won't be enough to fix u1 and u2. One will need two boundary conditions for that.
  4. Jul 3, 2012 #3
    I need more than the general solution
  5. Jul 3, 2012 #4


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    Have you tried solving it yourself?
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