Yuming Paul Zhang

I am an Assistant Professor at Department of Mathematics & Statistics, Auburn University.

Before joining Auburn, I was a SEW Assistant Professor at the Mathematics Department of UCSD, and my mentor is Prof. Andrej Zlatoš. In June 2019, I completed my PhD at UCLA , under the supervision of Prof. Inwon Kim.

I specialize in Partial Differential Equations (PDEs). My research interests include: Homogenization, Free boundary problems, Porous Medium Type Equations, Hamilton Jacobi equations, Control problems, Chemotaxis Models, Mean Field Games and Reaction-diffusion Equations. Here is my CV (June 2025). 

Le Chen, Bingyang Hu and I are organizing Seminars on Analysis and Stochastic Analysis (SASA) . 

I am organizing Applied and Computational Mathematics Seminars.  

Publications and preprints

• Preprints

  1. A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization, with O. Turanova, preprint 2025.

• 2. Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning, with Y. Zhu, H. Zhang, preprint 2025.

Preprint, 2025.

• 3. Policy iteration for nonconvex viscous Hamilton--Jacobi equations, with X. Guo, H. V. Tran, preprint, 2025.
      

• Publications

  1. Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models, with J. Tong, J. Math. Pures Appl., 203 (2025) 103752.

  2. The convergence rate of vanishing viscosity approximations for mean field games, with W. Tang, SIAM J. Math. Anal., 57.3 (2025): 3217-3254.
      

  3. The spreading of global solutions of chemotaxis systems with logistic source and consumption on ℝn , with Z. Hassan, W. Shen, Calc. Var. Partial Differential Equations, 64(2025) no.135. 

  4. Policy Iteration for Exploratory Hamilton–Jacobi–Bellman Equations, with H. V. Tran, Z. Wang, Appl. Math. Optim., 91(2025) no. 50. 

  5. Systemic robustness: a mean-field particle system approach, with E. Bayraktar, G. Guo, W. Tang, Mathematical Finance, (2025). 

  6. Policy iteration for the deterministic control problems -- a viscosity approach, with W. Tang, H. V. Tran, SIAM J. Control Optim., 63.1 (2025): 375-401. 

  7. Regularity of Hele-Shaw Flow with source and drift, with I. Kim, Annals of PDE 10.2 (2024): 20. 

  8. Global existence of classical solutions of chemotaxis systems with logistic source and consumption or linear signal production on ℝn , with Z. Hassan, W. Shen, Journal of Differential Equations 413 (2024): 497-556. 

  9. Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations, with A. Zlatoš, Calc. Var. Partial Differential Equations, 62 (2023), no. 9, 238. 

  10. Subadditive Theorems and First Passage Percolation in Time-Dependent Environments, with A. Zlatoš, Electron. J. Probab., 28(2023) no. 96, 1-23. 

  11. Optimal Estimates on the Propagation of Reactions with Fractional Diffusion, with A. Zlatoš, Arch. Ration. Mech. Anal., 247(2023) no. 5, 93.

  12. McKean-Vlasov Equations Involving Hitting Times: Blow-ups and Global Solvability, with E. Bayraktar, G. Guo, W. Tang, Ann. Appl. Probab., 34 (2024) no. 1B, 1600-1622. 

  13. Quantitative Homogenization for Combustion in Random Media, with A. Zlatoš, Ann. Inst. H. Poincaré Anal. Non Linéaire, (2023).

  14. Exploratory HJB Equations and Their Convergence, with W. Tang, X. Y. Zhou, SIAM J. Control Optim., 60 (2022) no. 6, 3191-3216.

  15. Long Time Dynamics for Combustion in Random Media, with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 1-62. 

  16. Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One, Calc. Var. Partial Differential Equations, 61(2022) no. 2, 1-35. 

  17. Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, Nonlinear Anal., 211(2021) 112413.

  18. Parallel Search for Information in Continuous Time -- Optimal Stopping and Geometry of the PDE, with T. T. Ke, W. Tang, J. M. Villas-Boas, Appl. Math. Optim., 85 (2022) no.2, 1-23.

  19. Porous Medium Equation with a Drift: Free boundary Regularity, with I. C. Kim, Arch. Ration. Mech. Anal., 242(2021) no.2, 1177-1228.

  20. Regularity Theory for Second Order Integro-PDEs, with C. Mou, Potential Anal., 54(2021) no.2 387-407.

  21. Continuity Properties for Divergence Form Boundary Data Homogenization Problems, with W. M. Feldman, Anal. PDE, 12(2019) no.8, 1963-2002.

  22. On a Class of Diffusion-Aggregation Equations, Discrete Contin. Dyn. Syst., 40(2020) no.2, 907.

  23. Regularity Properties of Degenerate Diffusion Equations with Drifts, with I. C. Kim, SIAM J. Math. Anal., 50(2018) no.4, 4371-4406. 

  24. On Continuity Equations in Space-Time Domains, Discrete Contin. Dyn. Syst., 38(2018) no.10, 4837-4873.

  25. On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains, J. London Math. Soc., 105 (2022) no. 2, 909-949.

  26. Lack of Exponential Decay in Viscoelastic Materials with Voids, with T. Xiao, Systems Control Lett., 63 (2014)39-42.