ON A CONTROL PROBLEM FOR MEMORY KERNELS IN HEAT CONDUCTION

Unger F.; Vonwolfersdorf L.

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ON A CONTROL PROBLEM FOR MEMORY KERNELS IN HEAT CONDUCTION

机译：导热核的控制问题

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A problem of identification of memory kernels in heat flow in a bar consisting of material with thermal memory is considered. The corresponding linear integrodifferential equation for the temperature contains a pair of time-dependent convolution kernels that are unknown. Such kernels are determined as solutions of an optimal control problem of least squares type by using additional data obtained from measurements of temperature in fixed points of the bar over some finite time interval. We derive optimality conditions for the memory kernels and give a numerical example for constructing them. [References: 7]

机译：考虑了在具有热记忆的材料组成的条中识别热流中的记忆核的问题。温度的相应线性积分微分方程包含一对未知的时间相关卷积核。通过使用从某个有限时间间隔内的棒固定点的温度测量获得的附加数据，可以将此类内核确定为最小二乘型最优控制问题的解决方案。我们推导了存储内核的最优条件，并给出了构建它们的数值示例。 [参考：7]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |1995年第5期|共6页
作者
Unger F.; Vonwolfersdorf L.;
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正文语种 eng
中图分类应用数学;
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Equation;

机译：方程;

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专利

1. ON A CONTROL PROBLEM FOR MEMORY KERNELS IN HEAT CONDUCTION [J] . Unger F., Vonwolfersdorf L. Zeitschrift fur Angewandte Mathematik und Mechanik . 1995,第5期

机译：导热核的控制问题
2. Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory [J] . Van Bockstal K., De Staelen R. H., Slodicka M. Journal of Computational and Applied Mathematics . 2015,第Null期

机译：半线性积分微分抛物线问题中记忆核的识别及其在记忆热传导中的应用
3. Steady-state heat conduction in a medium with spatial non-singular fading memory: Derivation of Caputo-Fabrizio space-fractional derivative from Cattaneo concept with Jeffrey`s Kernel and analytical solutions [J] . Hristov Jordan Thermal science . 2017,第2期

机译：具有空间非奇异衰落记忆的介质中的稳态导热：由Cattaneo概念和Jeffrey的核导出Caputo-Fabrizio空间分数导数和解析解
4. Exact Controllability of the Heat Equation with Hyperbolic Memory Kernel [C] . Jiongmin Yong, Xu Zhang Conference on Control Theory for Partial Differential Equations . 2005

机译：具有双曲记忆核的热方程的精确可控性
5. Studies in isothermal heat conduction calorimetry: I. The 2-drop calorimeter and educational applications. II. The quartz crystal microbalance/heat conduction calorimeter (QCM/HCC) and applications in studying the thermodynamic and rheological properties of polymer and protein thin films at a solid-gas interface. [D] . Mulligan, Rose B. 2002

机译：等温热传导量热法的研究：I.两滴量热仪和教育应用。二。石英晶体微天平/热传导量热仪（QCM / HCC）及其在研究固-气界面处聚合物和蛋白质薄膜的热力学和流变特性方面的应用。
6. Fructan biosynthesis and degradation as part of plant metabolism controlling sugar fluxes during durum wheat kernel maturation [O] . Sara Cimini, Vittoria Locato, Rudy Vergauwen, 2015

机译：在硬粒小麦籽粒成熟过程中果聚糖生物合成和降解是控制糖通量的植物代谢的一部分
7. Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory [O] . Van Bockstal Karel, De Staelen Rob, Slodicka Marian 2015

机译：半线性积分微分抛物问题中存储核的识别及其与存储器热传导的应用

ON A CONTROL PROBLEM FOR MEMORY KERNELS IN HEAT CONDUCTION

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