具边界控制和同位观测的变系数薛定谔传递方程的适定正则性

邵志超,张小燕

系统科学与数学 ›› 2016, Vol. 36 ›› Issue (8) : 1068-1080.

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系统科学与数学 ›› 2016, Vol. 36 ›› Issue (8) : 1068-1080. DOI: 10.12341/jssms12849
论文

具边界控制和同位观测的变系数薛定谔传递方程的适定正则性

    邵志超,张小燕
作者信息 +

WELL-POSEDNESS AND REGULARITY OF SCHR\"{O}DINGER TRANSMISSION EQUATION WITH VARIABLE COEFFICIENTS UNDER BOUNDARY CONTROL AND COLLOCATED OBSERVATION

    SHAO Zhi-Chao ,ZHANG Xiaoyan
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摘要

考虑具有 Dirichlet 边界控制和同位观测的高维变系数 Schr\"odinger 传递方程系统. 证明了该系统在 Salamon 的意义下是适定的, 在 Weisse 意义下为正则的, 且直接传输算子为零. 黎曼几何方法被用来处理变系数所带来的困难.

Abstract

This paper considers the system governed by multidimensional Schr\"{o}dinger transmission equation with variable coefficients under Dirichlet boundary control and collocated observation. It is proved that this system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. Moreover, the feedthrough operator is zero. Riemannian geometrical approach is adopted to deal with the difficulty brought by the variable coefficients.

关键词

适定性 / 正则性 / 薛定谔方程 / 传递问题 / 黎曼几何方法.

Key words

Well-posedness, regularity, Schr\" / {o}dinger equation, transmission problem, Riemannian geometrical approach.

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邵志超 , 张小燕. 具边界控制和同位观测的变系数薛定谔传递方程的适定正则性. 系统科学与数学, 2016, 36(8): 1068-1080. https://doi.org/10.12341/jssms12849
SHAO Zhi-Chao , ZHANG Xiaoyan. WELL-POSEDNESS AND REGULARITY OF SCHR\"{O}DINGER TRANSMISSION EQUATION WITH VARIABLE COEFFICIENTS UNDER BOUNDARY CONTROL AND COLLOCATED OBSERVATION. Journal of Systems Science and Mathematical Sciences, 2016, 36(8): 1068-1080 https://doi.org/10.12341/jssms12849
中图分类号: 93C20    34G10   
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