52 citations · 85 across the 10 of their papers we have counts for
9 papers · 1 filter
On regularity of averaged Green's functions in homogenization of elliptic PDE
Joseph G. Conlon, Michael Dabkowski
This paper is concerned with establishing estimates on averaged Green's functions for a uniformly elliptic divergence form partial difference equation with random coefficients on t…
On Global Asymptotic Stability for the diffusive Carr-Penrose Model
Joseph G. Conlon, Michael Dabkowski
This paper is concerned with large time behavior of the solution to a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. Like the LSW model, the Carr-Pe…
On Properties of the Dirichlet Green's function for linear diffusions on a half line
Joseph G. Conlon, Michael Dabkowski
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know…
On Global Asymptotic Stability for the LSW Model with subcritical initial data
Joseph G. Conlon, Michael Dabkowski
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic sta…
Global Stability for a Class of Nonlinear PDE with non-local term
Joseph G. Conlon, Michael Dabkowski
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner mo…
On large time behavior and selection principle for a diffusive Carr-Penrose Model
Joseph G. Conlon, Michael Dabkowski, Jingchen Wu
This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the prese…
Global well-posedness of slightly supercritical active scalar equations
Michael Dabkowski, Alexander Kiselev, Luis Silvestre +1
The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasi-geostrophic (SQG) and Burgers e…
Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
Michael Dabkowski, Alexander Kiselev, Vlad Vicol
We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velo…
Eventual Regularity of the Solutions to the Supercritical Dissipative Quasi-Geostrophic Equation
Michael Dabkowski
Recently, Silvestre proved that certain weak solutions of the slightly supercritical surface quasi-geostrophic equation eventually become smooth. To prove this, he employed a De Gi…