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Singular ordinary differential equations homogeneous of degree 0 near a codimension $ 2$ set


Authors: D. Bresch, B. Desjardins and E. Grenier
Journal: Proc. Amer. Math. Soc. 140 (2012), 1697-1704
MSC (2010): Primary 37N10, 35A05, 74H35
DOI: https://doi.org/10.1090/S0002-9939-2011-11044-X
Published electronically: December 27, 2011
MathSciNet review: 2869153
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Abstract: This paper deals with an example of a class of ordinary differential equations which are singular near a codimension $ 2$ set with a homogeneous singularity of degree 0. Under some structural assumptions, we prove that for almost all initial data there exists a unique global solution.


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Additional Information

D. Bresch
Affiliation: LAMA, UMR5127 CNRS, Université de Savoie, 73376 Le Bourget du lac, France
Email: Didier.bresch@univ-savoie.fr

B. Desjardins
Affiliation: ENS Ulm, D.M.A., 45 rue d’Ulm, 75230 Paris cedex 05, France – and – Modélisation Mesures et Applications S.A., 66 avenue des Champs Elysées, 75008 Paris, France
Email: Benoit.Desjardins@mines.org

E. Grenier
Affiliation: U.M.P.A., École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon Cedex 07, France
Email: egrenier@umpa.ens-lyon.fr

DOI: https://doi.org/10.1090/S0002-9939-2011-11044-X
Keywords: Singular ODE’s, codimension 2 singularity, global existence and uniqueness, low Mach number limit
Received by editor(s): March 25, 2009
Received by editor(s) in revised form: February 4, 2010, and January 20, 2011
Published electronically: December 27, 2011
Communicated by: Walter Craig
Article copyright: © Copyright 2011 American Mathematical Society