TY - JOUR
T1 - Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biasing force process
AU - Alrachid, Houssam
AU - Lelièvre, Tony
AU - Talhouk, Raafat
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/5/5
Y1 - 2016/5/5
N2 - We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non-linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result.
AB - We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non-linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result.
KW - Adaptive biasing force
KW - Fokker-Planck
KW - Nonlocal nonlinearity
UR - https://www.scopus.com/pages/publications/84958613072
U2 - 10.1016/j.jde.2016.01.020
DO - 10.1016/j.jde.2016.01.020
M3 - Article
AN - SCOPUS:84958613072
SN - 0022-0396
VL - 260
SP - 7032
EP - 7058
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 9
ER -