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Yuming Paul Zhang
Department of Mathematics and Statistics
COSAM Auburn University
Office : 204 Parker Hall
Email: yzhangpaul" at "auburn.edu
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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, Reaction-diffusion 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
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Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models, with J. Tong, preprint, 2024.
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Global existence of classical solutions of chemotaxis systems with logistic source and consumption or linear signal production on ℝn , with Z. Hassan, W. Shen, preprint, submitted, 2023.
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The convergence rate of vanishing viscosity approximations for mean field
games, with W. Tang, preprint, submitted, 2023.
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Policy iteration for the deterministic control problems -- a viscosity approach, with W. Tang, H. V. Tran, preprint, submitted, 2023.
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Systemic robustness: a mean-field particle system approach, with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2022.
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Regularity of Hele-Shaw Flow with source and drift, with I. Kim, preprint, 2022.
Publications
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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.
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Subadditive Theorems and First Passage Percolation in Time-Dependent Environments, with A. Zlatoš, Electron. J. Probab., 28(2023) no. 96, 1-23.
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Optimal Estimates on the Propagation of Reactions with Fractional Diffusion,
with A. Zlatoš, Arch. Ration. Mech. Anal., 247(2023) no. 5, 93.
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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.
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Quantitative Homogenization for Combustion in Random Media,
with A. Zlatoš, Ann. Inst. H. Poincaré Anal. Non Linéaire, (2023).
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Exploratory HJB Equations and Their Convergence,
with W. Tang, X. Y. Zhou, SIAM J. Control Optim., 60 (2022) no. 6, 3191-3216.
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Long Time Dynamics for Combustion in Random Media,
with A. Zlatoš, Arch. Ration. Mech. Anal., (2021) 1-62.
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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.
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Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, Nonlinear Anal., 211(2021) 112413.
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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.
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Porous Medium Equation with a Drift: Free boundary Regularity,
with I. C. Kim,
Arch. Ration. Mech. Anal., 242(2021) no.2, 1177-1228.
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Regularity Theory for Second Order Integro-PDEs, with C. Mou,
Potential Anal., 54(2021) no.2 387-407.
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Continuity Properties for Divergence Form Boundary Data Homogenization Problems,
with W. M. Feldman, Anal. PDE, 12(2019) no.8, 1963-2002.
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On a Class of Diffusion-Aggregation Equations,
Discrete Contin. Dyn. Syst., 40(2020) no.2, 907.
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Regularity Properties of Degenerate Diffusion Equations with Drifts,
with I. C. Kim, SIAM J. Math. Anal., 50(2018) no.4, 4371-4406.
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On Continuity Equations in Space-Time Domains,
Discrete Contin. Dyn. Syst., 38(2018) no.10, 4837-4873.
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On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains,
J. London Math. Soc., 105 (2022) no. 2, 909-949.
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Lack of Exponential Decay in Viscoelastic Materials with Voids,
with T. Xiao, Systems Control Lett., 63 (2014)39-42.