Geodesic
Penalty method to solve an optimal control problem for a quasilinear parabolic equation
Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 2, pp. 158-163

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An optimal control problem for a quasilinear parabolic equation simulating the radiative and conductive heat transfer in a bounded three-dimensional domain under constraints on the solution in a given subdomain is considered. The solvability of the optimal control problem is proved. An algorithm for solving the problem, based on the penalty method, is proposed. 
@article{DVMG_2022_22_2_a3,
     author = {A. Yu. Chebotarev and N. M. Park and P. R. Mesenev and A. E. Kovtanyuk},
     title = {Penalty method to solve an optimal control problem for a quasilinear parabolic equation},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {158--163},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2022_22_2_a3/}
}
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A. Yu. Chebotarev; N. M. Park; P. R. Mesenev; A. E. Kovtanyuk. Penalty method to solve an optimal control problem for a quasilinear parabolic equation. Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 2, pp. 158-163. http://geodesic.mathdoc.fr/item/DVMG_2022_22_2_a3/