## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Sliding Vector Fields via Slow--Fast Systems

#### Abstract

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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 5 (2008), 851-869.

Dates
First available: 5 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.bbms/1228486412

Mathematical Reviews number (MathSciNet)
MR2484137

Zentralblatt MATH identifier
05496980

#### Citation

Llibre, Jaume; da Silva, Paulo R.; Teixeira, Marco A. Sliding Vector Fields via Slow--Fast Systems. Bulletin of the Belgian Mathematical Society - Simon Stevin 15 (2008), no. 5, 851--869. http://projecteuclid.org/euclid.bbms/1228486412.