very complicated green function

[logistic_guy]

$\displaystyle \large \frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2} + Q(x,t)$

$\displaystyle \large u(0,t) = 0$
$\displaystyle \large u(L,t) = 0$
$\displaystyle \large u(x,0) = g(x)$


Find the green function $\displaystyle \large G(x,t;x_0,t_0)$.

 

[khansaheb]

$\displaystyle \large \frac{\partial u}{\partial t} = k\frac{\partial^2 u}{\partial x^2} + Q(x,t)$

$\displaystyle \large u(0,t) = 0$
$\displaystyle \large u(L,t) = 0$
$\displaystyle \large u(x,0) = g(x)$


Find the green function $\displaystyle \large G(x,t;x_0,t_0)$.

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