Scientific Research

Research Field

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Paper Publications

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• Michel Cristofol,Shumin Li,Yunxia Shang.Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by partial boundary layer data. Part II: Some inverse problems.[J].Mathematical Methods in the Applied Sciences,46(12):13304–13319.
• Xue Qin,Shumin Li.Local logarithmic stability of an inverse coefficient problem for a singular heat equation with an inverse-square potential.[J].Applicable Analysis,2023,102(7):1995–2017.
• Shumin Li,Yunxia Shang.Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by boundary data. Part I: Carleman estimates.[J].Journal of Inverse and Ill-Posed Problems,2022,30(5):621-658.
• Xue Qin,Shumin Li.The null controllability for a singular heat equation with variable coefficients.[J].Applicable Analysis,2022,101(3):1052-1076.
• Yunxia Shang,Shumin Li.Conditional stability in a backward Cahn-Hilliard equation via a Carleman estimate.[J].Journal of Inverse and Ill-Posed Problems,2021,29(2):159-171.
• Yunxia Shang,Shumin Li.Control properties for second-order hyperbolic systems in anisotropic cases with applications in inhomogeneous and anisotropic elastodynamic systems.[J].SIAM Journal on Control and Optimization,2018,56(6):4181-4202.

Patents

• NAKAGAWA Junichi,ITO Tadayuki,YAMAMOTO Masahiro,LI Shumin,TAKEUCHI Tomoya,TAN Yongji,Invent,METHOD FOR ESTIMATING AMOUNT OF DUSTFALL, DEVICE FOR ESTIMATING AMOUNT OF DUSTFALL, AND PROGRAM FOR ESTIMATING AMOUNT OF DUSTFALL,PCT/JP2009/062035,2009-07-01,2010-01-07,WO 2010/001925 A1,

Published Books

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Research Projects

• 双曲型方程组反问题及脉冲输入法反波速问题研究,完成,
• 二阶双曲型方程组的Carleman估计及其在麦克斯韦方程组反问题中的应用,完成,
• 关于强耦合双曲型方程组的小系数反问题及其相关课题的数学分析,进行,
• 关于非各项同性介质中双曲型方程组的反问题的数学解析,完成,