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Radial-spherical coordinates. Transient 1-D.

The Heat Equation for transient 1-D Green's Functions in radial-spherical coordinates is:

$\displaystyle {\frac{1}{r^{2}}}$$\displaystyle {\frac{\partial }{\partial r}}$$\displaystyle \left(\vphantom{ r^{2}\frac{\partial G}
{\partial r}}\right.$r2$\displaystyle {\frac{\partial G}{\partial r}}$ $\displaystyle \left.\vphantom{ r^{2}\frac{\partial G}
{\partial r}}\right)$ + $\displaystyle {\frac{1}{\alpha }}$$\displaystyle \delta$(r - r$\scriptstyle \prime$)$\displaystyle \delta$(t - $\displaystyle \tau$) = $\displaystyle {\frac{1}{\alpha }}$$\displaystyle {\frac{\partial G}{\partial t}}$    

The radial-spherical Dirac delta function $ \delta$(r - r$\scriptstyle \prime$) has vector arguments and has units of [ meters-3].


Kevin D. Cole