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Second-order non-linear PDE

  1. Sep 22, 2009 #1
    I've run across a PDE that (since I've failed to take a PDE class!) I'm finding some difficulty in solving. Does anyone have any suggestions? It's on a function R(r,t), with functions a(r,t) and b(r,t) and a constant k. If it's easier to solve with a and b not having t-dependence (just being a(r) and b(r)) I'd be curious to know - I'm not sure if that affects things.

    Here's the PDE:

    R = k(-e-2a Rtt + e-2b Rrr +[ar + br + 2/r] e-2b Rr)

    I'd really appreciate any help! I have a couple of ways of attacking this problem (I also have R defined in terms of derivatives of a and b) but I think a solution to this PDE in terms of a, b, r, and t would be incredibly useful. Thanks!
  2. jcsd
  3. Sep 23, 2009 #2
    Sorry - the first term (the derivatives in t) disappear. I don't expect any t dependence, so this is really just an ODE in r. Still, any advice would be appreciated :)
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