We investigate the general Porous Medium Equations with drift and source terms that model
tumor growth. Incompressible limit of such models has been well-studied in the literature …

We establish regularity and, under suitable assumptions, convergence to stationary states
for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation …

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 are interested in studying the stationary solutions and phase transitions of aggregation
equations with degenerate diffusion of porous medium-type, with exponent 1< m< ∞ 1< …

We prove the existence and Sobolev regularity of solutions of a nonlinear system of
degenerate-parabolic PDEs with self-and cross-diffusion, transport/confinement and …

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≤ …

Flow of an ideal gas through a homogeneous porous medium can be described by the well-
known Porous Medium Equation (PME). The key feature is that the pressure is proportional …

We investigate the diffusion-aggregation equations with degenerate diffusion $\Delta u^ m $
and singular interaction kernel $\mathcal {K} _s=(-\Delta)^{-s} $ with $ s\in (0,\frac {d}{2}) …

In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate
diffusion-drift equations in the form of ut= Δ u m+∇⋅ B (x, t) u, for m≥ 1 assuming a vector …

We investigate a generalized Hele–Shaw equation with a source and drift terms where the
density is constrained by an upper-bound density constraint that varies in space and time …