Optimal multiplicative control of a semilinear parabolic equation

An analysis of optimal control problems for a nonlinear parabolic initial-boundary value problem that models the dynamics of the collective behavior of a bacterial community is presented. Estimates for the solution of the initial-boundary value problem are obtained, the solvability of control problems is proved, and optimality conditions are derived. The weak «bang-bang» principle is set for the problem with the final observation.