Differential equations close to the intersection of two discontinuity surfaces (Ernst Hairer, UniGe)

13.10.2015 14:15

This talk considers ordinary differential equations with discontinuous right-hand side, where the discontinuity of the vector field takes place on smooth hyper-surfaces of the phase space. Solutions may traverse a hyper-surface, but they can also stick in them (Filippov’s sliding mode).

In the case of non-uniqueness of solutions a standard regularization permits to select the most meaningful one. A complete classification of possible transitions of solutions close to the intersection of two discontinuity surfaces is given. The result is sometimes counterintuitive.

This is joint work with Nicola Guglielmi from the University of L’Aquila. More details can be found in the publication
N. Guglielmi and E. Hairer, Classification of hidden dynamics in discontinuous dynamical systems, SIAM J. Appl. Dyn. Syst. 14(3) (2015) 1454-1477.
It can be downloaded from my homepage
http://www.unige.ch/~hairer/preprints.html

Lieu

salle 623, Séminaire d'analyse numérique

entrée libre