On the limit solution of regularized piecewise-smooth dynamical systems
Nicola Guglielmi and Ernst Hairer,
Abstract. This work deals with piecewise-smooth dynamical systems and with
regularizations, where the jump discontinuities in the vector field are smoothed out
in an $\eps$-neighbourhood by using a continuous transition function. It addresses the
questions whether the solution of the regularization converges to a Filippov solution
of the discontinuous problem, and under which condition the limit for $\eps\to 0$
of the regularized solution is independent of the transition function. The results are complemented
by numerical simulations.
Key Words. Regularization, discontinuous dynamical system, Filippov solution.