Yuming Paul Zhang
Papers and preprints (back)
Homogenization
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Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations, with A. Zlatoš, preprint, submitted, 2022.
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Quantitative Homogenization for Combustion in Random Media, with A. Zlatoš, preprint, submitted, 2021.
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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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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 Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains,
J. London Math. Soc., 105 (2022) no. 2, 909-949.
Free boundary problems
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McKean-Vlasov Equations Involving Hitting Times: Blow-ups and Global Solvability,
with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2020.
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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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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.
Regularity problmes
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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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Regularity Theory for Second Order Integro-PDEs, with C. Mou,
Potential Anal., 54(2021) no.2 387-407.
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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.
Front propagation and Subadditive theorems
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Subadditive Theorems and First Passage Percolation in Time-Dependent Environments, with A. Zlatoš, preprint, submitted, 2022.
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Optimal Estimates on the Propagation of Reactions with Fractional Diffusion,
with A. Zlatoš, preprint, submitted, 2021.
Gradient flow and Stability results
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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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Exploratory HJB Equations and Their Convergence,
with W. Tang, X. Y. Zhou,
preprint, submitted, 2021.
Semi-group method
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Lack of Exponential Decay in Viscoelastic Materials with Voids,
with T. Xiao, Systems Control Lett., 63 (2014)39-42.