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Any hope for this PDE? Diffusion in population genetics 
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#1
Mar310, 11:34 PM

P: 1

I'm working on a problem in multiallele diffusion in population genetics and I have come to this PDE:
[tex]0 = (tp_1(1p_1)sp_2)\frac{\partial u}{\partial p_1}+(sp_2(1p_2)tp_1)\frac{\partial u}{\partial p_2} + \frac{p_1(1p_1)}{2}\frac{\partial^2 u}{\partial p_1^2} + \frac{p_2(1p_2)}{2}\frac{\partial^2 u}{\partial p_2^2}  p_1p_2 \frac{\partial^2 u}{\partial p_1 \partial p_2}[/tex] The boundary conditions are u(0,p2) = 0 (for all p2), u(1,0) = 1 I'm not entirely sure it's possible to solve, though it's highly symmetric so I thought I'd give it a shot and see if anyone has any ideas. I tried separating which obviously doesn't work (unless I'm a failure) and I've spent some time searching for clever transformations that might work, but it seems to be of no use :( Thanks! 


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