Geodesic
Optimal multiplicative control of a semilinear parabolic equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 270-277.

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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. 
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A. Yu. Chebotarev. Optimal multiplicative control of a semilinear parabolic equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 270-277. http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a12/

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