Li Desheng
School
School of Mathematics
Professional Title
Professor
Contact Information
lidsmath@tju.edu.cn
Brief Introduction
1998年6月毕业于兰州大学数学系, 获理学博士学位, 2000年6月北京师范大学数学所博士后出站；2000年7月-2005年6月先后担任烟台大学副教授、教授；2005年7月至今任天津大学数学学院教授、博士生导师。
主要从事非线性微分方程和动力系统以及非线性控制系统的动力学理论方面的工作。已主持完成国家自然科学基金面上项目4项、省部级基金项目2项，在国际著名数学期刊《SIAM J Cont. Optim.》、《SIAM J Appl. Dyn. Syst.》、《Indian Univ Math J》、《J Diff. Eqns.》和《Disc. Cont. Dyn. Syst.》等杂志发表论文30余篇。
代表性工作有：1. 建立了具有快速增涨非线性项的Cahn-Hilliard系统吸引子的存在性，解决了著名数学家R.Temam关于该系统的有关开问题，相关论文已被全文录入专著《Global attractor in abstract parabolic problems》(J.W. Cholewa, T. Dlotko著, 剑桥大学出版社, 2000), 同时被著名数学家 G.R. Sell和 Y.C. You 等人的专著所收录；2. 建立了隐式微分方程的Peano定理和延拓定理；3. 建立了非光滑系统吸引子的Morse理论,并从该角度给出了非线性开环系统控制集的Morse刻划；4. 建立了动力系统的环绕定理和山路定理；5. 给出了非线性发展方程的新的局部和全局动态分支定理。
Academic Achievements
- Papers
- [1] Li Desheng, Wang Zhiqiang, Local and global dynamic bifurcations of nonlinear evolution equations, Indiana Univ. Math. J., 2017, in press.
- [2] Li Chunqiu, Li Desheng*, Zhang Zhijun, Dynamic Bifurcation from Infinity of Nonlinear EvolutionEquations, SIAM J Appl. Dyn. Systems, 2017, to appear. (* Corresponding author)
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- [3] Wang Jintao, Li Desheng*, Duan jinqiao, On the shape Conley index theory of semiflows on complete metric spaces, Disc. Cont. Dyan. Systems-A, 36 (2), pp1629-1647, 2016. (Corresponding author)
- [4] Li Desheng, Qi Ailing, Morse equation of attractors for nonsmooth dynamical systems, J.Diff. Eqns., 253 (11), pp 3081-3100, 2012.
- [5] Li Desheng, Wang Yanling, Smooth Morse-Lyapunov functions of strong attractors for differential inclusions, SIAM J. Cont. Optim., 50 (1), pp 368-387, 2012.
- [6] Li Desheng, Ju Xuewei, On the dynamical behavior of viscous Cahn-Hilliard equation, Disc. Cont. Dyan. Systems-A, 32 (6), pp 2207-2221, 2012.
- [7] Li Desheng, Duan Jinqiao, Structure of the set of bounded solutions for a class of nonautonomoussecond-order differential equations, J. Diff. Eqns., 246(5), pp 1754–1773, 2009.
- [8] Li Desheng, Morse decompositions for general dynamical systems and differential inclusions withapplications to control systems, SIAM J. Cont. Optim., 46(1), pp 35-60,2007.
- [9] Li Desheng, P. E. Kloeden, On the dynamics of nonautonomous periodic general dynamical systems anddifferential inclusions, J. Diff. Eqns.,224 (1), pp 1– 38, 2006.
- [10] Li Desheng, P. E. Kloeden, Robustness of asymptotic stability to small time delays, Disc. Cont. Dyn.Systems, 13 (4), 1007–1034, 2005.
- [11] Li Desheng, Peano's theorem for implicit differential equations, J. Math. Anal. Appl., 258(2), pp 591-616, 2001.
- [12] Li Desheng, Zhong Chengkui, Global attractor for the Cahn-Hilliard system with fast growing nonlinearity, J. Diff. Eqns., 149 (1), 191-210，1998.