三维抛物型微分包含第一类混合边值问题的Optimization
Optimization of the first mixed boundary value problem for parabolic differential inclusions in a three spatial dimension
摘要：
研究了抛物型微分包含（DFI）第边值问题的Laplace算子优化问题。为此，定义了一个抛物离散包含问题，这是主要的辅助问题。利用局部伴随映射，证明了抛物离散包含最优性的充要条件。然后，利用抛物型DFI的离散化方法和已有的离散包含最优性条件，给出了Euler-Lagrange型包含形式的离散近似问题的充要条件.因此，使用专门证明的等价定理，没有它几乎不可能得到所需的结果所提出的问题，我们建立充分的最优性条件的抛物型DFI。为了证明上述方法，一些线性问题和多面体优化抛物型夹杂物进行了研究。
英文摘要：
The paper is devoted to the optimization of a first mixed boundary value problem for parabolic differential inclusions (DFIs) with Laplace operator. For this, a problem with a parabolic discrete inclusion is defined, which is the main auxiliary problem. With the help of locally adjoint mappings, necessary and sufficient conditions for the optimality of parabolic discrete inclusions are proved. Then, using the method of discretization of parabolic DFIs and the already obtained optimality conditions for discrete inclusions, the necessary and sufficient conditions for the discrete-approximate problem are formulated in the form of the Euler-Lagrange type inclusion. Thus, using specially proved equivalence theorems, without which it would hardly be possible to obtain the desired result for the problem posed, we establish sufficient optimality conditions for a parabolic DFIs. To demonstrate the above approach, some linear problems and polyhedral optimization with inclusions of parabolic type are investigated.
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