共查询到19条相似文献,搜索用时 250 毫秒
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应用Hille-Yosida定理研究了无穷维Hamilton算子,得到了一个无穷维Hamilton系统初值问题解的存在性定理,并把结果应用在由一类双曲型偏微分方程导出的无穷维Hamilton系统中,给出了此类无穷维Hamilton系统解的存在性定理. 相似文献
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本文研究斜对角无穷维Hamilton算子$H=\begin{pmatrix}0&B\\C&0\end{pmatrix}$的点谱和特征函数系辛结构的非退化性, 给出斜对角无穷维Hamilton算子$H$的特征函数系具有非退化辛结构的充分必要条件. 基于此, 进一步刻画了斜对角无穷维Hamilton算子$H$的点谱分别包含于实轴、虚轴以及其它区域的充分必要条件. 最后, 以板弯曲问题和弦振动问题中导出的斜对角无穷维Hamilton算子为例, 验证了所得结论的正确性. 相似文献
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本文研究了无穷维Hamilton算子的可逆性问题,进而,刻画了无穷维Hamilton算子的谱的分布,并运用内部的逆紧性描述了无穷维Hamilton算子的逆紧性.最后,给出了无穷维Hamilton算子的可逆性问题在Dirac算子的可逆性问题中的应用. 相似文献
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讨论了一类无穷维Hamilton算子的Fredholm性,由于无穷维Hamilton算子是分块算子矩阵,将它的Fredholm性用它的元素算子的某种组合来描述,给出了无穷维Hamilton算子是Fredholm算子的充分必要条件. 相似文献
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本文运用算子扰动理论研究了无穷维Hamilton算子的共轭算子,进而得到了无穷维Hamilton算子为辛自伴算子的若干充分条件. 相似文献
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无穷维Hamilton算子特征函数系是否完备与其代数指标有关,研究了上三角无穷维Hamilton算子特征值的代数指标问题,基于主对角元的特征值和特征向量的某些性质,得到上三角无穷维Hamilton算子的几何重数和代数重数. 相似文献
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The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem. 相似文献
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O. I. Mokhov 《Theoretical and Mathematical Physics》2002,133(2):1557-1564
We prove that two Dubrovin–Novikov Hamiltonian operators are compatible if and only if one of these operators is the Lie derivative of the other operator along a certain vector field. We consider the class of flat manifolds, which correspond to arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. Locally, these manifolds are defined by solutions of a system of nonlinear equations, which is integrable by the method of the inverse scattering problem. We construct the integrable hierarchies generated by arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. 相似文献
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一类无穷维Hamilton算子的半群生成定理 总被引:3,自引:0,他引:3
研究了无穷维H am ilton算子生成C0半群的问题,得到了类无穷维H am ilton算子生成C0半群的一个充分条件.把结果应用在一类双曲型混合问题生成的无穷维H am ilton算子上,证明此类算子生成C0半群,并利用H ille-Y osida定理进一步说明了结果的正确性和有效性.另外,还给出了波动方程相应的无穷维H am ilton算子所生成的C0半群的具体表达式. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(10):3779-3789
We discuss at first in this paper the Gauge equivalence among several u‐linear Hamiltonian operators and present explicitly the associated Gauge transformation of Bäcklund type among them. We then establish the sufficient and necessary conditions for the linear superposition of the discussed u‐linear operators and matrix differential operators with constant coefficients of arbitrary order to be Hamiltonian, which interestingly shows that the resulting Hamiltonian operators survive only up to the third differential order. Finally, we explore a few illustrative examples of integrable hierarchies from Hamiltonian pairs embedded in the resulting Hamiltonian operators. 相似文献
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本文讨论了极限圆型Hamilton算子乘积的自伴性,利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论,给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件. 相似文献
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本文讨论了一类在弦和梁的微小振动中出现的二次算子族L(λ)=λ~2MλK-A的谱分布问题,进而将所得结论与无穷维Hamilton算子联系起来,利用无穷维Hamilton算子的特殊结构,得到了一类非负无穷维Hamilton算子的谱分布,这为无穷维Hamilton算子的半群方法提供了理论保证. 相似文献
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Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献