We establish the H\" older continuity of bounded nonnegative weak solutions to\begin
{align*}\big (\Phi^{-1}(w)\big) _t=\Delta w+\nabla\cdot\big (a (x, t)\Phi^{-1}(w)\big)+ b\big (x …

We study regularity properties of the free boundary for solutions of the porous medium
equation with the presence of drift. We show the C 1, α regularity of the free boundary when …

We study porous medium equations with a divergence form of drift terms in a bounded
domain with no-flux lateral boundary conditions. We establish L q-weak solutions for 1≤ …

We consider degenerate porous medium equations with a divergence type of drift terms. We
establish existence of nonnegative L q-weak solutions (satisfying energy estimates or even …

We consider nonlinear drift-diffusion equations (both porous medium equations and fast
diffusion equations) with a measure-valued external force. We establish existence of …

This paper studies the large time behavior of aggregation-diffusion equations. For one
spatial dimension with certain assumptions on the interaction potential, the diffusion index …

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 …

The continuity equation concerned in this paper is a degenerate-diffusion equation with a
non-local drift. The equation is studied in space dimension one. Under the assumption that …