- #1
jhartc90
- 43
- 0
Homework Statement
I have a PDE and I need to solve it in spherical domain:
$$\frac{dF(r,t)}{dt}=\alpha \frac{1}{r^2} \frac{d}{dr} r^2 \frac{dF(r,t)}{dr} +g(r,t) $$
I have BC's:
$$ \frac{dF}{dr} = 0, r =0$$
$$ \frac{dF}{dr} = 0, r =R$$
Homework Equations
So, in spherical coord.
First, I know that:
$$F=w/r$$
Reducing, I get:
$$\frac{dw}{dt} =\alpha \frac{d^2w}{dr^2}+r*g(r,t) $$
The Attempt at a Solution
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After I Get this, I need to find eigenfunction expansions to express the source term and
then, finally, the solution Do I need to do separation of variables? I am confused at this point and not sure how to proceed.