I have to study the controllability of this equation
$\frac{\partial u}{\partial t}(t,x)=\dfrac{\partial^{2} u}{\partial x^{2}}(t,x)+f(u)+c(t,x)$
where $c$ is a control acting in the whole domain $\Omega$. I saw for reference to that problem, but I found research that study controls acting in a open strict subset of $\Omega$.
Where I can find some references for this problem?
Thanks for your answers.