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Singular ordinary differential equations homogeneous of degree 0 near a codimension  set
Authors:
D. Bresch, B. Desjardins and E. Grenier
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1697-1704
MSC (2010):
Primary 37N10, 35A05, 74H35
Posted:
December 27, 2011
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Abstract: This paper deals with an example of a class of ordinary differential equations which are singular near a codimension  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.
References
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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:
http://dx.doi.org/10.1090/S0002-9939-2011-11044-X
PII:
S 0002-9939(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
Posted:
December 27, 2011
Communicated by:
Walter Craig
Article copyright:
© Copyright 2011 American Mathematical Society
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