Sliding Vector Fields via Slow--Fast Systems

This paper concerns differential equation systems on \mathbb R^n with discontinuous right--hand sides. We deal with non-smooth vector fields in \mathbb R^n having a codimension-one submanifold M as its discontinuity set. After a regularization of a such system and a global blow-up we are able to bri...

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Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2008-01, Vol.15 (5), p.851-869
Main Authors: Llibre, Jaume, Teixeira, Marco A., da Silva, Paulo R.
Format: Article
Language:English
Subjects:
34C20
34C26
34D15
34H05
discontinuous vector fields
Regularization
singular perturbation
sliding vector fields
vector fields
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Summary:This paper concerns differential equation systems on \mathbb R^n with discontinuous right--hand sides. We deal with non-smooth vector fields in \mathbb R^n having a codimension-one submanifold M as its discontinuity set. After a regularization of a such system and a global blow-up we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1228486412