Hi I'd appreciate any help on identifying the type of PDE the following equation is...(adsbygoogle = window.adsbygoogle || []).push({});

*This is NOT homework, it is part of research and thus the lack my explanation of what this represents and boundary conditions. I have a numerical simulation of the solution but I'm looking to have a math win on my thesis.*

dC/dt = D(del^2(C)+[itex]y_{1}[/itex]del(σ))

I've used seperation of variables into a space function and a temporal function (which I've already solved since it's the exact same as the standard Diffusion equation). Long story short this is very similar to a Sturm-Louisville Problem but instead of getting a characteristic equation with lambda squared times the space function I end up with after subbing in the conditions for sigma.

d^2U/dr^2+(1/r)dU/dr+(ψ*δ(r-[itex]r_{0}[/itex])+λ^2)*U=0

I have two issues with getting a solution here first is the dirac delta before the eigenvalues (lambda) and second is that I have no idea what type of PDE this falls under other than it is very similar to S-L problems. I'm positive that the solution will include bessel functions (as you can probably tell this is in cylindrical.

If someone could point me to the type of PDE or even better a text that I could reference for this type's solution method you would make my day.

Cheers.

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# Modified diffusion equation PDE

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