Hi, I'm trying to find an analytical solution (if one exists) to the 1d diffusion equation with variable diffusivity κ(x);(adsbygoogle = window.adsbygoogle || []).push({});

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\partial_t u(x,t) = \partial_x[\kappa(x) \partial_x u(x,t)]

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Could someone point me in the right direction to solve this if its possible to do so analytically. I've tried separation of variables after using the product rule to expand out the diffusive term but the equation isn't of the correct form.

Thanks for any advice,

Kieran

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# Analytical solution to the diffusion equation with variable diffusivity

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