Radial heat equation in three dimensions ($u_t=D{r}^{-1}(ru{)}_{rr}$)

For a spherically symmetric field $u(r,t)$ in three dimensions,Thus the heat equation becomes $u_t=D{r}^{-1}(ru{)}_{rr}$. Introducing $w=ru$ reduces its spatial part to the one-dimensional second derivative $w_{rr}$, while regularity at the centre requires $w(0,t)=0$.