
Yuming Paul Zhang
Department of Mathematics and Statistics
COSAM Auburn University
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.
I specialize in Partial Differential Equations (PDEs). My research interests include: Homogenization, Reactiondiffusion equations, Free boundary problems, Porous Medium Type Equations, Hamilton Jacobi equations, Control problems, Chemotaxis Models and Mean Field Games.
Here is my CV (Feb 2024).
Le Chen and I are organizing
Seminars on Analysis and Stochastic Analysis (SASA).
Publications and preprints (sorted by area)
Preprints

Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models, with J. Tong, preprint, 2024.

Global existence of classical solutions of chemotaxis systems with logistic source and consumption or linear signal production on ℝ^{n }, with Z. Hassan, W. Shen, preprint, submitted, 2023.

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 meanfield particle system approach, with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2022.

Regularity of HeleShaw Flow with source and drift, with I. Kim, preprint, 2022.
Publications

Homogenization for SpaceTimeDependent KPP ReactionDiffusion Equations and GEquations, with A. Zlatoš, Calc. Var. Partial Differential Equations, 62 (2023), no. 9, 238.

Subadditive Theorems and First Passage Percolation in TimeDependent Environments, with A. Zlatoš, Electron. J. Probab., 28(2023) no. 96, 123.

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

McKeanVlasov Equations Involving Hitting Times: Blowups and Global Solvability,
with E. Bayraktar, G. Guo, W. Tang, Ann. Appl. Probab., 34 (2024) no. 1B, 16001622.

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

Exploratory HJB Equations and Their Convergence,
with W. Tang, X. Y. Zhou, SIAM J. Control Optim., 60 (2022) no. 6, 31913216.

Long Time Dynamics for Combustion in Random Media,
with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 162.

Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One,
Calc. Var. Partial Differential Equations, 61(2022) no. 2, 135.

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. VillasBoas, Appl. Math.
Optim., 85 (2022) no.2, 123.

Porous Medium Equation with a Drift: Free boundary Regularity,
with I. C. Kim,
Arch. Ration. Mech. Anal., 242(2021) no.2, 11771228.

Regularity Theory for Second Order IntegroPDEs, with C. Mou,
Potential Anal., 54(2021) no.2 387407.

Continuity Properties for Divergence Form Boundary Data Homogenization Problems,
with W. M. Feldman, Anal. PDE, 12(2019) no.8, 19632002.

On a Class of DiffusionAggregation 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, 43714406.

On Continuity Equations in SpaceTime Domains,
Discrete Contin. Dyn. Syst., 38(2018) no.10, 48374873.

On Homogenization Problems with Oscillating Dirichlet Conditions in SpaceTime Domains,
J. London Math. Soc., 105 (2022) no. 2, 909949.

Lack of Exponential Decay in Viscoelastic Materials with Voids,
with T. Xiao, Systems Control Lett., 63 (2014)3942.