scholarly journals An elementary approach to uniform in time propagation of chaos

2020 ◽  
Vol 148 (12) ◽  
pp. 5387-5398
Author(s):  
Alain Durmus ◽  
Andreas Eberle ◽  
Arnaud Guillin ◽  
Raphael Zimmer
Keyword(s):  
Propagation Of Chaos ◽  
Elementary Approach ◽  
Time Propagation

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model

2016 ◽  
Vol 166 (2) ◽  
pp. 211-229 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Qitao Yin
Keyword(s):  
Flow Model ◽  
Mean Field ◽  
Propagation Of Chaos ◽  
Pedestrian Flow ◽  
Field Limit ◽  
Mean Field Limit

Patterns of time propagation on the grid of potential curves

1998 ◽  
Vol 58 (6) ◽  
pp. 4293-4299 ◽  
Author(s):  
Valentin N. Ostrovsky ◽  
Hiroki Nakamura
Keyword(s):  
Time Propagation ◽  
Potential Curves

On Grothendieck's local duality theorem

1979 ◽  
Vol 85 (3) ◽  
pp. 431-437 ◽  
Author(s):  
M. H. Bijan-Zadeh ◽  
R. Y. Sharp
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Noetherian Ring ◽  
Duality Theorem ◽  
Great Emphasis ◽  
Triangulated Category ◽  
Elementary Approach ◽  
Commutative Noetherian Ring ◽  
Local Duality ◽  
Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

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