势算子理论对线性耦合热弹性动力学的应用
APPLICATION OF POTENTIAL OPERATOR THEORY IN LINEAR COUPLED THERMO-ELASTODYNAMICS
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摘要: 本文的主要目的在于从下面两个方向研究耦合问题极小化方法:(1)建立两个耦合热弹性动力学的最小值原理;(2)为广泛一类耦合物理系统提供构造极小化泛函的具体步骤。基本思想是:(1)通过消元法和卷积理论减少控制方程数目;(2)通过在Banach空间上的有势算子理论分离耦合变量;(3)导出在Laplace变换的象空间上的转换最小值原理;(4)通过引进相容权函数的集合构造原空-时间域的极小化泛函。文中的结果对构造广泛的一类耦合系统极小化泛函具有重要意义。Abstract: The main objective of this paper is to study minimization methods for coupled problems in the following two directions:(1)to establish two minimum principles for the coupled thermo-elastodynamics:(2)to provide, for a wide class of coupled physical systems,an algorithm to construct the appropriate minimization functions.The main idea of the paper consists in the following steps:(1) to reduce the number of governing equations by elimination and the convolution theory;(2) to separate coupled variables using potential operator defined in a real Banach space ;(3) to derive a transformed minimum principle for Laplace transformation;(4) to establish the minimizing functional by the introduction of the set of admissible weight functions to the original space-time domain . The results of this paper are of great significance on constructing minimizing functionals for a wide class of coupled systems.
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Keywords:
- coupling problem /
- potential operator /
- seperation /
- minimum principle
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