This is a report on project initiated with Anne Nouri [3], presently in progress, with the collaboration of Nicolas Besse [2] ([2] is mainly the material of this report) . It concerns a version of the Vlasov equation where the self interacting potential is replaced by a Dirac mass. Emphasis is put on the relations between the linearized version, the full non linear problem and also on natural connections with several other equations of mathematical physic.
Claude Bardos. About a Variant of the $1d$ Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation". Séminaire Laurent Schwartz — EDP et applications (2012), Talk no. 15, 21 p.. doi: 10.5802/slsedp.42
@article{SLSEDP_2012-2013____A15_0,
author = {Claude Bardos},
title = {About a {Variant} of the $1d$ {Vlasov} equation, dubbed {{\textquotedblleft}Vlasov-Dirac-Benney} {Equation"}},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:15},
pages = {1--21},
year = {2012-2013},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
doi = {10.5802/slsedp.42},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.42/}
}
TY - JOUR AU - Claude Bardos TI - About a Variant of the $1d$ Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation" JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:15 PY - 2012-2013 SP - 1 EP - 21 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.42/ DO - 10.5802/slsedp.42 LA - en ID - SLSEDP_2012-2013____A15_0 ER -
%0 Journal Article %A Claude Bardos %T About a Variant of the $1d$ Vlasov equation, dubbed “Vlasov-Dirac-Benney Equation" %J Séminaire Laurent Schwartz — EDP et applications %Z talk:15 %D 2012-2013 %P 1-21 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.42/ %R 10.5802/slsedp.42 %G en %F SLSEDP_2012-2013____A15_0
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