Title | Optimization of two-dimensional heating processes taking into account phase limitations |
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Authors | N. D. Morozkin^{1}, V. I. Tkachev^{1}, Y. N. Morozkin^{1}^{1}Ufa University of Science and Technology |

Annotation | The problems of time-optimal control of the processes of external heating of a rectangular prism and a cylinder of finite length are studied under restrictions on the highest temperature and on thermal stresses. Dependences of ultimate compressive and tensile strengths on temperature are taken into account, which are approximated by convex functions. The original infinite-dimensional problem is approximated by a finite-dimensional time-optimal problem with convex phase constraints. Estimates of the error of approximations by the state in space are written out. In the absence of restrictions on thermal stresses, the convergence of finite-dimensional approximations in terms of the speed functional and the weak convergence of the sequence of controls to the optimal control are shown. |

Keywords | optimal heating, thermal stresses, speed, rectangular prism, cylinder of finite length |

Citation | Morozkin N. D., Tkachev V. I., Morozkin Y. N. ''Optimization of two-dimensional heating processes taking into account phase limitations'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 160-165. Available at: https://conf.svmo.ru/files/2023/papers/paper25.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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