2 papers
math.AP2019
Regularity of solutions of a fractional porous medium equation
Cyril Imbert, Rana Tarhini, François Vigneron
This article is concerned with a porous medium equation whose pressure law is both nonlinear and nonlocal, namely $\partial_t u = { \nabla \cdot} \left(u \nabla(-Δ)^{\fracα{2}-1}u^…
math.AP2015
Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin film equation
Rana Tarhini
In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for 0<α<2. The equation is a generalization of the one arising in the modeling of hydraulic fracture…