2019/12/19 by Domingo A. Tarzia, Tarzia, Domingo A., Carolina M. Bollo +3
Computer Science · Mathematics · #35K05 #49J20 #49K20 #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1912.09157
openalex publication_date 2019/12/19 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider a heat conduction problem S with mixed boundary conditions in a\nn-dimensional domain \Ω with regular boundary \Γ and a family of\nproblems S\α, where the parameter \α>0 is the heat transfer\ncoefficient on the portion of the boundary \Γ1. In relation to these\nstate systems, we formulate simultaneous \distributed-boundary optimal\ncontrol problems on the internal energy g and the heat flux q on the\ncomplementary portion of the boundary \Γ2. We obtain existence and\nuniqueness of the optimal controls, the first order optimality conditions in\nterms of the adjoint state and the convergence of the optimal controls, the\nsystem and the adjoint states when the heat transfer coefficient \α goes\nto infinity. Finally, we prove estimations between the simultaneous\ndistributed-boundary optimal control and the distributed optimal control\nproblem studied in a previous paper of the first author.\n