A spatial domain decomposition method for parabolic optimal control problems (Q869527)

The authors introduce a new spatial domain decomposition method for the solution of linear-quadratic parabolic optimal control problems of the form \[ \begin{multlined}\text{minimize }{\alpha_1\over 2} \int^T_0 \int_\Omega (y(x, t)-\widehat y(x, t))^2\,dx\,dt+\\ {\alpha_2\over 2} \int_\Omega (y(x, T)-\widehat y_T(x))^2\,dx+ {\alpha_3\over 2} \int^T_0 \int_\Omega u^2(x, t)\,dx\,dt\end{multlined} \] \[ \begin{multlined}\text{subject to }\partial_t y(x, t)-\mu\Delta y(x, t)+ a(x)\cdot\nabla y(x,t)+\\ c(x) y(x,t)= f(x,t)+ u(x, t)\qquad\text{in }\Omega\times (0,T),\end{multlined} \] \[ y(x,t)= 0\quad\text{on }\partial\Omega\times (0, T),\qquad y(x,0)= y_0(x)\qquad\text{in }\Omega. \]