[SOLVED] Diffusion equation with a death rate

**wglmb** · November 15th 2009, 02:29 PM

I've been given this equation:

$\frac{\partial n}{\partial t} = D_0 \frac{\partial}{\partial x}\left [ \left ( \frac{n}{n_0} \right ) ^m \frac{\partial n}{\partial x} \right ]- \mu n, D_0>0, \mu >0$

(where " $- \mu n$ " is the death term)

Then I'm told:
Suppose $n(x,0) = Q\delta (x)$ . Show by appropriate transformations in $n$ and $t$ that this question can be reduced to one equivalent to

$\frac{\partial n}{\partial t} = D_0 \frac{\partial}{\partial x}\left [ \left ( \frac{n}{n_0} \right ) ^m \frac{\partial n}{\partial x} \right ]$

ie with no death term.

Now, I have absolutely no idea what transformations to use...

**wglmb** · November 16th 2009, 06:06 AM

Not to worry; the answer is to transform $n$ to $ne^{-\mu t}$

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