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

Education

Ph. D., Mathematics, Nanjing University, 1999.
B.S., Mathematics, Nanjing University, 1994.

Publications (2010-)

  1. Cannarsa, Piermarco; Cheng, Wei; Hong, Jiahui; Topological and control theoretic properties of Hamilton–Jacobi equations via Lax-Oleinik commutators. Nonlinear Anal. Real World Appl. 84 (2025), Paper No. 104282.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Cheng, W.; Hong, J.;Local strict singular characteristics: Cauchy problem with smooth initial data. J. Differential Equations 328 (2022), 326-353.
  7. 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.
  8. Cannarsa, P.; Cheng, W.; Local singular characteristics on \(\mathbb{R}^2\). Boll. Unione Mat. Ital. 14 (2021), no. 3, 483–504.
  9. Cannarsa, P.; Cheng, W., Singularities of Solutions of Hamilton–Jacobi Equations. Milan J. Math. 89 (2021), no. 1, 187-215.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Chen, C.; Cheng, W.; Zhang, Q., Lasry-Lions approximations for discounted Hamilton-Jacobi equations. J. Differential Equations 265 (2018), no. 2, 719-732.
  19. Cannarsa, P.; Cheng, W., Generalized characteristics and Lax-Oleinik operators: global theory. Calc. Var. Partial Differential Equations 56 (2017), no. 5, 56:125.
  20. 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.
  21. Chen, C.; Cheng, W., Lasry-Lions, Lax-Oleinik and generalized characteristics. Sci. China Math. 59 (2016), no. 9, 1737-1752.
  22. Cannarsa, P.; Cheng, W., Homoclinic orbits and critical points of barrier functions. Nonlinearity 28 (2015), no. 6, 1823-1840.
  23. 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.
  24. Cheng, W., Generalized Maupertuis' principle with applications. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 11, 2153-2160.
  25. Cheng, W., On Mather's \(\alpha\)-function of mechanical systems. Proc. Amer. Math. Soc. 139 (2011), no. 6, 2143-2149.
  26. Cheng, W., The integrability of positively definite Lagrangian systems via variational criterion: mechanical systems. J. Differential Equations 249 (2010), no. 7, 1664-1673.

Preprints

  1. Cheng, W.; Hong, J.; Shi, T., Optimal transport in the frame of abstract Lax-Oleinik operator revisited, preprint, arXiv:2402.04159, 2024.
  2. Cheng, W.; Wei, W., A geometric approach to Mather quotient problem, preprint, arXiv:2409.00958, 2024.
  3. Cannarsa, P; Cheng, W.; Hong, J.; Wang, K., Variational construction of singular characteristics and propagation of singularities, preprint, arXiv:2409.00961, 2024.
  4. Cannarsa, P.; Cheng, W.; Mendico, C., Long time behaviour of generalised gradient flows via occupational measures, preprint, arXiv:2410.20943, 2024.
  5. Cheng, W.; Hong, J.; Zhu, Z.-X., Qualitative estimates of topological entropy for non-monotone contact Lax-Oleinik semiflow, preprint, arXiv:2412.15087, 2024.
  6. Cannarsa, P;, Cheng, W.; Shi, T.; Wei, W., Singularities and their propagation in optimal transport, preprint, arXiv:2501.15605, 2025.

Conference

  1. Inverse Problems and Control for PDEs and the Hamilton-Jacobi Equation, June 13-17, 2022, Centre International de Rencontres Mathématiques, Marseille, France.
  2. Weak KAM theory - XXV+1 years later, May 30-June 3, 2022, Avignon Université, Avignon, France.
  3. VIII Partial differential equations, optimal design and numerics, Aug 18-30, 2019, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain.
  4. Conference on PDEs, Dynamical Systems and Probability, February 21-22, 2019, Kodaira, Japan.
  5. CIMPA school on dynamical systems, October 25 - November 6, 2018, Kathmandu, Nepal.
  6. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5-9, 2018, Taipei.
  7. Gran Sasso Science Institute (GSSI) workshop on ``New trends in control of evolution system'', April 19-21, 2018, L'Aquila, Italy.
  8. 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.
  9. The first annual meeting of International Consortium of Chinese Mathematicians, December 27-29, 2017, Guangzhou, China.
  10. International Conference on Singularity Theory and Dynamical Systems - in Memory of John Mather, December 11-15, 2017, Sanya, China.
  11. 2017 Chengdu workshop on differential dynamical systems, December, 8-20, 2017, Chengdu, China.
  12. SIAM Conference on Control and Its Applications, July 10-12, 2017, Pittsburgh, Pennsylvania, US.
  13. New trends in Control Theory and PDEs, Istituto Nazionale di Alta Matematica (INdAM), July 3-7, 2017, Rome, Italy.
  14. Beyond Hamilton-Jacobi, Last call to Bordeaux, January, 9-13, 2017, Bordeaux, France.
  15. SIAM conference on Analysis of partial Differential Equations, December, 2015, Scottsdale, Arizona, US.
  16. INdAM Workshop "Hamilton-Jacobi equation: at the crossroads of PDE, Dynamical Systems and Geometry", June, 2015, Cortona, Italy.
  17. Workshop on Hamiltonian dynamical systems, January, 2015, Shanghai, China.
  18. International Congress of Chinese Mathematicians, July, 2013, Taipei.
  19. Conference on Dynamics and Transport in Disordered Systems, June, 2011, Toronto, Canada.
  20. 12th Frontier Science Symposium, November, 2011, Singapore.

Slides

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

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