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Laplace equation: \nabla^2 u = 0,\quad \mbox{1D: } u''(x)=0
Poisson equation: -\nabla^2 u = f,\quad \mbox{1D: } -u''(x)=f(x)
These are limiting behavior of time-dependent diffusion equations if \lim_{t\rightarrow\infty}\frac{\partial u}{\partial t} = 0
Then u_t = \dfc u_{xx} + 0 in the limit t\rightarrow\infty reduces to u_{xx} + f = 0
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