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**Creebe** The following partial differential equation describes the radially symmetric temperature distribution in the annulus $\displaystyle 0<a<r<b$, with constant temperature prescribed at $\displaystyle r=a$ and $\displaystyle r=b$:

$\displaystyle u_t = \frac{1}{r} (ru_r)_r$

$\displaystyle a<r<b, t>0$

Boundary Conditions:

$\displaystyle u(a,t) = 0, u(b,t)=1$

Initial Condition:

$\displaystyle u(r,0) = f(r)$

Find the steady-state temperature distribution $\displaystyle v(r) = \lim_{ t \to \infty} u(r,t)$

Please help...it's due tomorrow.