Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions

2021/06/25 by Harbir Antil, Antil, Harbir, Shodai Kubota +5
Chemical Engineering · Engineering · #35K51 #49J20 #49K20 #74N05 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Metallurgy and Material Forming #Optimization and Control (math.OC) #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2106.13373

openalex publication_date 2021/06/25 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a class of optimal control problems governed by state-equations of Kobayashi--Warren--Carter type. The control is given by physical temperature. The focus is on problems in dimensions less than equal to 4. The results are divided in four Main Theorems, concerned with: solvability and parameter-dependence of state-equations and optimal control problems; the first order necessary optimality conditions for these regularized optimal control problems. Subsequently, we derive the limiting systems and optimality conditions and study their well-posedness.

Citations

• A class of parabolic systems associated with optimal controls of grain\n boundary motions

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