Large time behavior for a nonlocal nonlinear gradient flow

Large time behavior of nonlocal aggregation models with nonlinear diffusion

The aim of this paper is to establish rigorous results on the large time behavior of nonlocal models for aggregation, including the possible presence of nonlinear diffusion terms modeling local repulsions. We show that, as expected from the practical motivation as well as from numerical simulations, one obtains concentrated densities (Dirac δ distributions) as stationary solutions and large tim...

Hölder Estimates and Large Time Behavior for a Nonlocal Doubly Nonlinear Evolution

A Three-terms Conjugate Gradient Algorithm for Solving Large-Scale Systems of Nonlinear Equations

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary st...