A note on control of one-dimensional heterogeneous reaction-diffusion equations

Abstract

We are concerned with the controllability of a general heterogeneous semilinear parabolic equation of the form \begin{document}$ y_t(x,t)=y_{xx}(x,t)+f(x,y(x,t)) $\end{document} in one space dimension using boundary static controls. More precisely, we provide conditions so that, using only static controls at the boundary, a certain target (a steady-state of the equation) is reached in infinite time. Applications of the main result are also presented, in particular, we provide several controllability results to heterogeneous equations of monostable and bistable types.