Studying a problem of difussion i came across the PDE (first order)(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \partial _{t} U(x,t) = U(x,t)^{2} [/tex]

with initial condition [tex] \partial _{t} U(x,0) = \delta (x) [/tex]

i have found the solution [tex] U(x,t)= \frac{ \delta (x) }{ t \delta (x) -1} [/tex]

however does this make sense ? from the definition of delta function the only values that U(x,t) can have for different positions 'x' are just 0 or infinity , and if i use a Taylor expansion i get

[tex] U(x,t)= - \delta (x) ( t\delta (x) +t^{2} (\delta (x) )^{2}+......) [/tex]

which makes no sense for me

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# A very odd partial differential equation.

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