Yuming Paul Zhang

Papers and preprints (back)

(Sep, 2025 update)

Reaction Diffusion Equations and Homogenization

• 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.
   
  
• Quantitative Homogenization for Combustion in Random Media, with A. Zlatoš, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2023.
   
  
• Long Time Dynamics for Combustion in Random Media, with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 1-62.
   
  
• Continuity Properties for Divergence Form Boundary Data Homogenization Problems, with W. M. Feldman, Anal. PDE, 12(2019) no.8, 1963-2002.
   
  
• On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains, J. London Math. Soc., 105 (2022) no. 2, 909-949.
   
  

  Free Boundary Problems

• A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization, with O. Turanova, preprint, 2025.
   
  
• Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models, with J. Tong, J. Math. Pures Appl., 203(2025) 103752.
   
  
• Regularity of Hele-Shaw Flow with source and drift, with I. Kim, Annals of PDE 10.2 (2024) 20.
   
  
• 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.
   
  
• 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.
   
  
• 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.
   
  
• Porous Medium Equation with a Drift: Free boundary Regularity, with I. C. Kim, Arch. Ration. Mech. Anal., 242(2021) no.2, 1177-1228.
   
  

Chemotaxis Model

• Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on ℝn: I. Global Solvability and Boundedness, with Z. Hassan, W. Shen, preprint, 2025.
   
  
• 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, 64.4(2025) 1-55.
   
  
• 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.
   
  
• Optimal Estimates on the Propagation of Reactions with Fractional Diffusion, with A. Zlatoš, Arch. Ration. Mech. Anal., 247(2023) no. 5, 93.
   
  

Optimal Control Problems and Learning

• Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning, with Y. Zhu, H. Zhang, preprint, 2025.
   
  
• Policy iteration for nonconvex viscous Hamilton--Jacobi equations, with X. Guo, H. V. Tran, preprint, 2025.
   
  
• Policy Iteration for Exploratory Hamilton–Jacobi–Bellman Equations, with H. V. Tran, Z. Wang, Appl. Math. Optim., 91(2025) no. 50.
   
  
• 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.
   
  
• Systemic robustness: a mean-field particle system approach, with E. Bayraktar, G. Guo, W. Tang, Mathematical Finance, (2025).
   
  
• Exploratory HJB Equations and Their Convergence, with W. Tang, X. Y. Zhou, SIAM J. Control Optim., 60 (2022) no. 6, 3191-3216.
   
  

Vanishing Viscosity Limit

• The convergence rate of vanishing viscosity approximations for mean field games, with W. Tang, SIAM J. Math. Anal., 57.3 (2025) 3217-3254.
   
  
• On Continuity Equations in Space-Time Domains, Discrete Contin. Dyn. Syst., 38(2018) no.10, 4837-4873.
   
  

Regularity Results

• Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, Nonlinear Anal., 211(2021) 112413.
   
  
• Regularity Theory for Second Order Integro-PDEs, with C. Mou, Potential Anal., 54(2021) no.2 387-407.
   
  
• On a Class of Diffusion-Aggregation Equations, Discrete Contin. Dyn. Syst., 40(2020) no.2, 907.
   
  
• Regularity Properties of Degenerate Diffusion Equations with Drifts, with I. C. Kim, SIAM J. Math. Anal., 50(2018) no.4, 4371-4406.
   
  

Subadditive Theorem

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

Porous Elastic System

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