17 citations · 34 across the 14 of their papers we have counts for
14 papers
Regularity of Hele-Shaw Flow with source and drift
Inwon Kim, Yuming Paul Zhang
In this paper we study the regularity property of Hele-Shaw flow, where source and drift are present in the evolution. More specifically we consider Hölder continuous source and Li…
Homogenization for Space-Time-Dependent KPP Reaction-Diffusion Equations and G-Equations
Yuming Paul Zhang, Andrej Zlatos
We prove stochastic homogenization for reaction-advection-diffusion equations with random space-time-dependent KPP reactions with temporal correlations that are decaying in an appr…
Quantitative Homogenization for Combustion in Random Media
Yuming Paul Zhang, Andrej Zlatos
We obtain the first quantitative stochastic homogenization result for reaction-diffusion equations, for ignition reactions in dimensions that either have finite ranges of…
Optimal Estimates on the Propagation of Reactions with Fractional Diffusion
Yuming Paul Zhang, Andrej Zlatos
We study the reaction-fractional-diffusion equation with ignition and monostable reactions , and . We obtain the first optimal bounds on the pro…
Long Time Dynamics for Combustion in Random Media
Yuming Paul Zhang, Andrej Zlatos
We study long time dynamics of combustive processes in random media, modeled by reaction-diffusion equations with random ignition reactions. One expects that under reasonable hypot…
Free Boundary Regularity of the Porous Medium Equation with nonlocal drifts in Dimension One
Yuming Paul Zhang
We study the free boundary of the porous medium equation with nonlocal drifts in dimension one. Under the assumption that the initial data has super-quadratic growth at the free bo…
Continuity results for degenerate diffusion equations with drifts
Sukjung Hwang, Yuming Paul Zhang
In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form \[ u_{t} = Δu^{m} + \nabla\cdot \left( B (x,t) \,…
Porous Medium Equation with A Drift: Free boundary Regularity
Inwon Kim, Yuming Paul Zhang
We study regularity properties of the free boundary for solutions of the porous medium equation with the presence of drift. We show the regularity of the free boundary, w…
Regularity theory for Second order Integro-PDEs
Chenchen Mou, Yuming Zhang
This paper is concerned with higher Hölder regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to \cite{mou2018}. We first obtain $C…
Continuity Properties for Divergence Form Boundary Data Homogenization Problems
William M. Feldman, Yuming Paul Zhang
We study the continuity/discontinuity of the effective boundary condition for periodic homogenization of oscillating Dirichlet data for nonlinear divergence form equations and line…
On a Class of Diffusion-Aggregation Equations
Yuming Zhang
We investigate the diffusion-aggregation equations with degenerate diffusion and singular interaction kernel with . We analy…
Regularity Properties of Degenerate Diffusion Equations with Drifts
Inwon Kim, Yuming Zhang
This paper considers a class of nonlinear, degenerate drift- diffusion equations. We study well-posedness and regularity properties of the solutions, with the goal to achieve unifo…
On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains
Yuming Paul Zhang
We prove the homogenization of fully nonlinear parabolic equations with periodic oscillating Dirichlet boundary conditions on certain general prescribed space-time domains. It was…
On Continuity Equations in Space-time Domains
Yuming Zhang
In this paper we consider a class of continuity equations that are conditioned to stay in general space-time domains, which is formulated as a continuum limit of interacting partic…