Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions
Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions
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发表时间：
2021-06
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通讯作者：
Harbir Antil;Sho Kubota;K. Shirakawa;N. Yamazaki
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作者：
Harbir Antil;Sho Kubota;K. Shirakawa;N. Yamazaki
本文考虑一类由Kobayashi-Warren-Carter类型的状态方程控制的最优控制问题。这种控制是由物理温度给出的。结果分为四个主要定理，涉及：状态方程和最优控制问题的可解性和参数依赖性；正则化最优控制问题的一阶必要条件。随后，我们得到了极限系统和最优性条件，并研究了它们的适定性。∗科学研究补助金(C)编号16K05224和编号20K03672的第三作者的作品。第四位作者的工作得到了科学研究助学金(C)编号20K03665的支持。此外，第一和第三作者的工作得到了空军科学研究办公室的部分支持，奖项编号：FA9550-19-1-0036，美国国家科学基金会拨款dms-1818772和dms-1913004。AMS科目分类：35K51、49J20、49K20、74N05。
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. ∗The work of the third author supported by Grant-in-Aid for Scientific Research (C) No. 16K05224 and No. 20K03672, JSPS. The work of the forth author supported by Grant-in-Aid for Scientific Research (C) No. 20K03665 , JSPS. In addition, the work of the first and the third authors is partially supported by the Air Force Office of Scientific Research (AFOSR) under Award NO: FA9550-19-1-0036 and NSF grants DMS-1818772 and DMS-1913004. AMS Subject Classification: 35K51, 49J20, 49K20, 74N05.