Wei Cheng's homepage
Wei Cheng (程伟)
Professor of Mathematics
School of Mathematics
Nanjing University
Contact Information:
E-mail: chengwei(at)nju.edu.cn
Teaching Schedule:
2024-2025 第一学期《常微分方程》习题
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.
Publications (2010-)
- Cheng, Wei; Hong, Jiahui; Local strict singular characteristics II: existence for stationary equations on $\mathbb{R}^2$. NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 5, Paper No. 64.
- Shi, T.; Cheng, W.; Hong, J.; Topology of singular set of semiconcave function via Arnaud's theorem. Commun. Pure Appl. Anal. 22 (2023), no. 6, 1950-1961.
- Cannarsa, Piermarco; Cheng, Wei; Mendico, Cristian; Wang, Kaizhi; Weak KAM Approach to First-Order Mean Field Games with State Constraints. J. Dynam. Differential Equations 35 (2023), no. 2, 1885-1916.
- Hong, J.; Cheng, W.; Hu, S.; Zhao, K., Representation Formulas for Contact Type Hamilton-Jacobi Equations. J. Dynam. Differential Equations 34 (2022), no. 3, 2315-2327.
- Cheng, W.; Hong, J.;Local strict singular characteristics: Cauchy problem with smooth initial data. J. Differential Equations 328 (2022), 326-353.
- 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.
Preprints
- Cannarsa, P; Cheng, W.; Hong, J., Topological and control theoretic properties of Hamilton-Jacobi equations via Lax-Oleinik commutators, preprint, arXiv:2311.07000, 2023.
- Cheng, W.; Hong, J.; Shi, T., Optimal transport in the frame of abstract Lax-Oleinik operator revisited, preprint, arXiv:2402.04159, 2024.
- Cheng, W.; Wei, W., A geometric approach to Mather quotient problem, preprint, arXiv:2409.00958, 2024.
- Cannarsa, P; Cheng, W.; Hong, J.; Wang, K., Variational construction of singular characteristics and propagation of singularities, preprint, arXiv:2409.00961, 2024.
Conference
- Inverse Problems and Control for PDEs and the Hamilton-Jacobi Equation, June 13-17, 2022, Centre International de Rencontres Mathématiques, Marseille, France.
- Weak KAM theory - XXV+1 years later, May 30-June 3, 2022, Avignon Université, Avignon, France.
- 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 "Hamilton-Jacobi equation: at the crossroads of PDE, Dynamical Systems and Geometry", June, 2015, Cortona, Italy.
- Workshop on Hamiltonian dynamical systems, January, 2015, Shanghai, China.
- International Congress of Chinese Mathematicians, July, 2013, Taipei.
- Conference on Dynamics and Transport in Disordered Systems, June, 2011, Toronto, Canada.
- 12th Frontier Science Symposium, November, 2011, Singapore.
Slides
- $\mathbb{R}^2$上的奇性特征线,上海交通大学,2020年5月.
Useful links