On Solvability of the Nonlinear Optimal Control Problem for Processes Described by the Semi-linear Parabolic Equations

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjoint boundary value problem of control process. It is established that optimal control is described as a solution of the complex structure nonlinear integral equation with additional condition in the form of the differential inequality, and the algorithm to determination of the optimal control was constructed. semi-linear parabolic equations, weak generalized solution, nonlinear optimization problem, optimality conditions, differential inequality, nonlinear integral equation of optimal control, factorization method.