TY - JOUR
T1 - A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
AU - A. Carrillo , José
AU - Chertock , Alina
AU - Huang , Yanghong
JO - Communications in Computational Physics
VL - 1
SP - 233
EP - 258
PY - 2018
DA - 2018/04
SN - 17
DO - http://doi.org/10.4208/cicp.160214.010814a
UR - https://global-sci.org/intro/article_detail/cicp/10957.html
KW - 
AB - <p style="text-align: justify;">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 states, different time
scales including metastability, as well as concentrations and self-similar behavior induced
by singular nonlocal kernels. We use the scheme to explore properties of these
equations beyond their present theoretical knowledge.</p>