Author:
Guglielmi Nicola,Hairer Ernst
Abstract
AbstractWe consider piecewise-smooth dynamical systems, i.e., systems of ordinary differential equations switching between different sets of equations on distinct domains, separated by hyper-surfaces. As is well-known, when the solution approaches a discontinuity manifold, a classical solution may cease to exist. For this reason, starting with the pioneering work of Filippov, a concept of weak solution (also known as sliding mode) has been introduced and studied. Nowadays, the solution of piecewise-smooth dynamical systems in and close to discontinuity manifolds is well understood, if the manifold consists locally of a single discontinuity hyper-surface or of the intersection of two discontinuity hyper-surfaces. The present work presents partial results on the solution in and close to discontinuity manifolds of codimension 3 and higher.
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Acary, V., Brogliato, B.: Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics. Lecture Notes in Applied and Computational Mechanics, vol. 35 Springer-Verlag (2008)
2. di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P.: Piecewise-smooth dynamical systems, vol. 163 of Applied Mathematical Sciences. Springer-Verlag London Ltd., London. Theory and applications (2008)
3. Dieci, L., Difonzo, F.: A comparison of Filippov sliding vector fields in codimension 2. J. Comput. Appl Math. 262, 161–179 (2014)
4. Dieci, L., Difonzo, F.: Minimum variation solutions for sliding vector fields on the intersection of two surfaces in $\mathbb {R},^{3}$. J. Comput. Appl Math. 292, 732–745 (2016)
5. Filippov, A.F.: Differential equations with discontinuous right-hand side. Mat. Sb. (N.S.) 51(93), 99–128 (1960). Amer. Math. Soc. Transl. Ser. 2, Vol. 42, pp. 199–231
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