A free boundary problem with nonlocal diffusion and unbounded initial range

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

quenching time for a nonlocal diffusion problem with large initial data

A free boundary problem for aggregation by short range sensing and differentiated diffusion

Abstract. On the d-dimensional torus we consider the drift-diffusion equation corresponding to the mean field limit of a stochastic model for direct aggregation which features a diffusion coefficient that depends on the locally measured empirical density. In particular, we consider the situation where the diffusion coefficient may take one of two possible values depending on whether the locally...

Initial-boundary Value Problem with a Nonlocal Condition for a Viscosity Equation

Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem

We consider a one-phase Stefan problem for the heat equation with a superlinear reaction term. It is known from a previous work (Ghidouche, Souplet, & Tarzia [5]) that all global solutions are bounded and decay uniformly to 0. Moreover, it was shown in Ghidouche, Souplet, & Tarzia [5] that either: (i) the free boundary converges to a finite limit and the solution decays at an exponential rate, ...