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Question about a parabolic PDE


phaedo

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Does anyone whether parabolic PDEs of the form:<br>

[math] u_t(x,t) = -a \cdot x(1-x)^2 u_x(x,t) + \frac {1} {2} b \cdot x^2(1-x)^2 u_{xx}(x,t) [/math]

<br>(a, b constants, t > 0, 0 < x < 1) have a closed-form fundamental solution?

Edited by phaedo
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