Yuming Paul Zhang
Department of Mathematics
9500 Gilman Dr, La Jolla, CA 92093
Office : AP&M 6305
Email: yzhangpaul" at "ucsd.edu
I am 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: Reaction-diffusion equations, Homogenization, Free Boundary Problems, Regularity Problems, and Optimal Transport.
Here is my CV (Apr 2021).
Papers and preprints
McKean-Vlasov equations involving hitting times: blow-ups and global solvability,
with E. Bayraktar, G. Guo, W. Tang, preprint, submitted, 2020.
Long Time Dynamics for Combustion in Random Media,
with A. Zlatoš, preprint, submitted, 2020.
Free Boundary Regularity of a Continuity Equation in Dimension One,
preprint, submitted, 2020.
Continuity Results for Degenerate Diffusion Equations with LqLp Drifts, with S. Hwang, preprint, submitted, 2019.
Parallel Search for Information, with T. T. Ke, W. Tang, J. M. Villas-Boas, preprint, submitted, 2019.
Porous Medium Equation with a Drift: Free boundary Regularity,
with I. C Kim, preprint, submitted, 2018.
Regularity Theory for Second Order Integro-PDEs, with C. Mou,
Potential Analysis (2020): 1-21.
Continuity Properties for Divergence Form Boundary Data Homogenization Problems,
with W. M. Feldman, Analysis & PDE 12.8 (2019): 1963-2002.
On a Class of Diffusion-Aggregation Equations,
Discrete & Continuous Dynamical Systems-A 40.2 (2020): 907.
Regularity Properties of Degenerate Diffusion Equations with Drifts,
with I. C Kim, SIAM J. Math. Anal. vol. 50(2018) no.4, 4371-4406.
On Continuity Equations in Space-Time Domains,
DCDS-A Vol. 38(2018) no.10, 4837-4873.
On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains,
preprint, submitted, 2017.
Lack of Exponential Decay in Viscoelastic Materials with Voids,
with T. Xiao, Systems & Control Letters 63 (2014)39-42.