I want to solve the following system of coupled differential equations:
$\frac{\partial f(x,t)}{\partial t}=b~\frac{\partial^{2}f(x,t)}{\partial x^{2}}-k~f(x,t)+g~ c(x,t)$
$\frac{\partial c(x,t)}{\partial t}=k~f(x,t)-g~c(x,t)$
with $f(x,0)=a$ and $c(x,0)=0$. The corresponding mathematica code is:
DSolve[{D[f[x, t], t] == b D[f[x, t], {x, 2}] - k f[x, t] + g c[x, t],
D[c[x, t], t] == k f[x, t] - g c[x, t], f[x, 0] == a, c[x, 0] == 0},
{f[x,t], c[x,t]}, {x, t}]
But the mathematica returns the code itself. Any idea how can I solve this?