This talk discusses the concept of solutions of piecewise smooth, discontinuous differential equations. Recent results of [1] are presented, which give new insight into the solution close to the intersection of two discontinuity hyper-surfaces. The study is connected to space regularizations where, close to the discontinuities, the vector field is smoothed out by linear (bi-linear) interpolation.

1.
N.
 
Guglielmi
, and
E.
 
Hairer
,
SIAM J. Appl. Dyn. Syst.
pp.
1
–
21
(
2016
).
Google Scholar
 
2.
A. F.
Filippov
 ,
Mat. Sb. (N.S.)
 
51
(
93
),
99
–
128
(
1960
),
Google Scholar
 
A. F.
 
Filippov
 
amer. Math. Soc. Transl. Ser. 2
, Vol.
42
, pp.
199
–
231
.
3.
A. F.
 
Filippov
,
Differential equations with discontinuous righthand sides, vol. 18 of Mathematics and its Applications (Soviet Series)
,
Kluwer Academic Publishers Group
,
Dordrecht
,
1988
, translated from the Russian.
Google Scholar
Crossref
Search ADS
 
4.
V.
 
Acary
, and
B.
 
Brogliato
, Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics,
Lecture Notes in Applied and Computational Mechanics
, Vol.
35
,
Springer-Verlag
,
2008
.
Google Scholar
 
5.
M.
 
di Bernardo
,
C. J.
 
Budd
,
A. R.
 
Champneys
, and
P.
 
Kowalczyk
,
Piecewise-smooth dynamical systems, vol. 163 of Applied Mathematical Sciences
,
Springer-Verlag London Ltd.
,
London
,
2008
, theory and applications.
Google Scholar
 
6.
J. C.
 
Alexander
, and
T. I.
 
Seidman
,
Houston J. Math.
 
24
,
545
–
569
(
1998
).
Google Scholar
 
7.
M. D.
 
Jeffrey
,
Phys. D
 
274–274
,
34
–
45
(
2014
).
https://doi.org/10.1016/j.physd.2014.02.003
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.