Wei Cheng （程伟）

Professor of Mathematics

Department of Mathematics

Nanjing University

Contact Information:

E-mail: chengwei(at)nju.edu.cn

- 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

Ph. D., Mathematics, Nanjing University, 1999.

B.S., Mathematics, Nanjing University, 1994.

- 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.

- 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 II: existence for stationary equation on \(\mathbb{R}^2\), preprint, arXiv:2202.13629, 2022.

- 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.

- \(\mathbb{R}^2\)上的奇性特征线，上海交通大学，2020年5月.

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