Coefficients for system of differential equations in pdetool

Dear people,

I have been struggling several days with Matlab and digging in the documentation to solve this system of parabolic equations.

du(1)/dt - div (c1* grad(u(1))) + (u(2)-u(1))*u(1) = 0
du(2)/dt - div (grad(u(2))) + u(1)*u(2) = 0
du(2)/dt = u(1)*u(2)

My solution now is

d = 1;  
c = [c1;1;0];
a = char('u(2)-u(1)','u(1)','0');
f = char('0','0','u(1)*u(2)');

and

u = parabolic(u0,tlist,b,p,e,t,c,a,f,d);

The solver gets a solution, but it is not what it should be. I wonder if I am not defining c,a, and f correctly. Any suggestion?