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I'm looking for solutions of a PDE of the form : $ P(t,x):[0,\infty]*[0,b]\rightarrow[0,1]$ $$ \partial_t P(t,x)= \partial_x [(1+2x) P(t,x)]$$ $$ P(0,x)=\delta_x (0)$$ $$P(t,b)=g(t)$$

Where $b$ is a boundary for $x$ and $g(t)$ is a known function. Is there anyone who knows how to solve this?

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    $\begingroup$ Change of variable $y=\log (2x+1)$? $\endgroup$ – Nemo Feb 17 at 6:32

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