个人简历

主要课程
《实变函数》
南京大学数学系教授，博导。目前主要研究领域为Hamilton动力系统，Aubry-Mather理论，Hamilton-Jacobi方程的粘性解理论，变分法与最优控制，平均场博弈论等。另外对几何测度论、sub-Riemannian几何、非光滑分析具有浓厚兴趣。在Comm. Math. Phys.，Calc. Var. Partial Differential Equations，Comm. Partial Differential Equations，SIAM J. Math. Anal.，J. Differential Equations，Dynamic Games and Applications等国际著名学术期刊发表20余篇论文。曾多次访问巴黎6大，巴黎7大，罗马2大，早稻田大学、国立新加坡大学，多次受邀在美国、法国、意大利、西班牙、日本、新加坡、台湾等地举办的国际学术会议上做学术报告。先后主持多项国家自然科学基金，作为骨干成员参加国家973项目，基金委重点项目。
Research interests
Hamiltonian dynamical systems: Mather theory and weak KAM theory
Hamilton-Jacobi equation: viscosity solutions, regularity
Calculus of variations and optimal control
Mean field games & Optimal transport
Riemannian and sub-Riemannian geometry
Nonsmooth analysis and geometric measure theory
Education
Ph. D., Mathematics, Nanjing University, 1999.
B.S., Mathematics, Nanjing University, 1994.
Preprints
Hong, J.; Cheng, W.; Hu, S.; Zhao, K., Representation formulas for contact type Hamilton-Jacobi equations, arXiv:1907.07542, 2019.
Cannarsa, P; Cheng, W.; Mendico, C.; Wang, K., Weak KAM approach to first-order Mean Field Games with state constraints, preprint, arXiv:2004.06505, 2020.
Cheng, W. and Hong, J., Local strict singular characteristics: Cauchy problem with smooth initial data, preprint, arXiv:2103.06217, 2021.
Conference
VIII Partial differential equations, optimal design and numerics, Aug 18-30, 2019, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain.
Conference on PDEs, Dynamical Systems and Probability, February 21-22, 2019, Kodaira, Japan.
CIMPA school on dynamical systems, October 25 - November 6, 2018, Kathmandu, Nepal.
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5-9, 2018, Taipei.
Gran Sasso Science Institute (GSSI) workshop on ``New trends in control of evolution system'', April 19-21, 2018, L'Aquila, Italy.
Gran Sasso Science Institute (GSSI) workshop on ``New developments on Hamilton-Jacobi Equations, Mean Field Games, and Weak KAM Theory'', March 2-3, 2018, L'Aquila, Italy.
The first annual meeting of International Consortium of Chinese Mathematicians, December 27-29, 2017, Guangzhou, China.
International Conference on Singularity Theory and Dynamical Systems - in Memory of John Mather, December 11-15, 2017, Sanya, China.
2017 Chengdu workshop on differential dynamical systems, December, 8-20, 2017, Chengdu, China.
SIAM Conference on Control and Its Applications, July 10-12, 2017, Pittsburgh, Pennsylvania, US.
New trends in Control Theory and PDEs, Istituto Nazionale di Alta Matematica (INdAM), July 3-7, 2017, Rome, Italy.
Beyond Hamilton-Jacobi, Last call to Bordeaux, January, 9-13, 2017, Bordeaux, France.
SIAM conference on Analysis of partial Differential Equations, December, 2015, Scottsdale, Arizona, US.
INdAM Workshop \

研究领域

"Hamilton动力系统，Hamilton-Jacobi方程、变分法与最优控制"

近期论文

Cannarsa, P.; Cheng, W.; Fathi, A.; Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry. Publ. Math. Inst. Hautes Études Sci. 133 (2021), no. 1, 327–366.
Cannarsa, P.; Cheng, W.; Local singular characteristics on \\(\\mathbb{R}^2\\). Boll. Unione Mat. Ital. 14 (2021), no. 3, 483–504.
Cannarsa, P.; Cheng, W., Singularities of Solutions of Hamilton–Jacobi Equations. Milan J. Math. 89 (2021), no. 1, 187-215.
Cannarsa, P.; Cheng, W., On and beyond propagation of singularities of viscosity solutions. Proceedings of the International Consortium of Chinese Mathematicians 2017, 141–157, Int. Press, Boston, MA, 2020.
Cannarsa, P.; Cheng, W.; Jin, L.; Wang, K.; Yan, J., Herglotz' variational principle and Lax-Oleinik evolution. J. Math. Pures Appl. (9) 141 (2020), 99–136.
Cannarsa, P.; Cheng, W.; Mendico, C.; Wang, K., Long-Time Behavior of First-Order Mean Field Games on Euclidean Space. Dyn. Games Appl. 10 (2020), no. 2, 361-390.
Cannarsa, P.; Cheng, W.; Mazzola, M.; Wang, K., Global Generalized Characteristics for the Dirichlet Problem for Hamilton–Jacobi Equations at a Supercritical Energy Level. SIAM J. Math. Anal. 51 (2019), no. 5, 4213-4244.
Cannarsa, P.; Cheng, W.; Wang, K.; Yan, J., Herglotz' generalized variational principle and contact type Hamilton-Jacobi equations. Trends in control theory and partial differential equations, 39-67, Springer INdAM Ser., 32, Springer, Cham, 2019.
Chen, Q.; Cheng, W.; Ishii, H.; Zhao, K., Vanishing contact structure problem and convergence of the viscosity solutions. Comm. Partial Differential Equations 44 (2019), no. 9, 801-836.
Cannarsa, P.; Chen, Q.; Cheng, W., Dynamic and asymptotic behavior of singularities of certain weak KAM solutions on the torus. J. Differential Equations 267 (2019), no. 4, 2448-2470.
Zhao, K..; Cheng, W., On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem. Discrete Contin. Dyn. Syst. 39 (2019), no. 8, 4345-4358.
Chen, C.; Cheng, W.; Zhang, Q., Lasry-Lions approximations for discounted Hamilton-Jacobi equations. J. Differential Equations 265 (2018), no. 2, 719-732.
Cannarsa, P.; Cheng, W., Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differential Equations 56 (2017), no. 5, 56:125.
Cannarsa, P.; Cheng, W.; Fathi, A., On the topology of the set of singularities of a solution to the Hamilton-Jacobi equation. C. R. Math. Acad. Sci. Paris 355 (2017), no. 2, 176-180.
Chen, C.; Cheng, W., Lasry-Lions, Lax-Oleinik and generalized characteristics. Sci. China Math. 59 (2016), no. 9, 1737-1752.
Cannarsa, P.; Cheng, W., Homoclinic orbits and critical points of barrier functions. Nonlinearity 28 (2015), no. 6, 1823-1840.
Cannarsa, P.; Cheng, W.; Zhang, Q., Propagation of singularities for weak KAM solutions and barrier functions. Comm. Math. Phys. 331 (2014), no. 1, 1-20.
Cheng, W., Generalized Maupertuis' principle with applications. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 11, 2153-2160.
Cheng, W., On Mather's \\(\\alpha\\)-function of mechanical systems. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2143-2149.
Cheng, W., The integrability of positively definite Lagrangian systems via variational criterion: mechanical systems. J. Differential Equations 249 (2010), no. 7, 1664-1673.