Yuming Paul Zhang
Department of Mathematics and Statistics
Office : 204 Parker Hall
Email: yzhangpaul" at "auburn.edu
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.
My research interests are: Stochastic homogenization, Reaction-diffusion equations, Free boundary problems, Hamilton Jacobi equations, Regularity problems, and Mean Field Games.
Here is my CV (Feb 2023).
Publications and preprints (sorted by area)
The convergence rate of vanishing viscosity approximations for mean field
games, with W. Tang, preprint, submitted, 2023.
Policy iteration for the deterministic control problems -- a viscosity approach, with W. Tang, H. V. Tran, preprint, submitted, 2023.
Systemic robustness: a mean-field particle system approach, with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2022.
Regularity of Hele-Shaw Flow with source and drift, with I. Kim, preprint, 2022.
Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations, with A. Zlatoš, preprint, submitted, 2022.
Subadditive Theorems and First Passage Percolation in Time-Dependent Environments, with A. Zlatoš, preprint, submitted, 2022.
Optimal Estimates on the Propagation of Reactions with Fractional Diffusion,
with A. Zlatoš, preprint, submitted, 2021.
McKean-Vlasov Equations Involving Hitting Times: Blow-ups and Global Solvability,
with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2020.
Quantitative Homogenization for Combustion in Random Media,
with A. Zlatoš, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
Exploratory HJB Equations and Their Convergence,
with W. Tang, X. Y. Zhou, SIAM J. Control Optim., to appear.
Long Time Dynamics for Combustion in Random Media,
with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 1-62.
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.
Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, Nonlinear Anal., 211(2021) 112413.
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.
Regularity Theory for Second Order Integro-PDEs, with C. Mou,
Potential Anal., 54(2021) no.2 387-407.
Continuity Properties for Divergence Form Boundary Data Homogenization Problems,
with W. M. Feldman, Anal. PDE, 12(2019) no.8, 1963-2002.
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.
On Continuity Equations in Space-Time Domains,
Discrete Contin. Dyn. Syst., 38(2018) no.10, 4837-4873.
On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains,
J. London Math. Soc., 105 (2022) no. 2, 909-949.
Lack of Exponential Decay in Viscoelastic Materials with Voids,
with T. Xiao, Systems Control Lett., 63 (2014)39-42.