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.(adsbygoogle = window.adsbygoogle || []).push({});

Here's the PDE:

R = k(-e^{-2a}R_{tt}+ e^{-2b}R_{rr}+[a_{r}+ b_{r}+ 2/r] e^{-2b}R_{r})

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!

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# Second-order non-linear PDE

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