# American Institute of Mathematical Sciences

April  2019, 39(4): 2255-2283. doi: 10.3934/dcds.2019095

## On smoothness of solutions to projected differential equations

 1 Lab. PROMES UPR CNRS 8521, Université de Perpignan Via Domitia, Rambla de la Thermodynamique, Tecnosud, F- 66100 Perpignan, France 2 Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, 163 rue Auguste Broussonnet, 34090 Montpellier, France 3 Instituto de Ciencias de la Educación, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile

* Corresponding author: David Salas

Received  August 2018 Revised  October 2018 Published  January 2019

Projected differential equations are known as fundamental mathematical models in economics, for electric circuits, etc. The present paper studies the (higher order) derivability as well as a generalized type of derivability of solutions of such equations when the set involved for projections is prox-regular with smooth boundary.

Citation: David Salas, Lionel Thibault, Emilio Vilches. On smoothness of solutions to projected differential equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2255-2283. doi: 10.3934/dcds.2019095
##### References:

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##### References:
Two prox-regular sets with smooth and non-smooth boundary
Sets of Definition 4.1 for a trajectory in $\mathbb{R} ^2$
A circuit with an ideal diode, an inductor and a current source
Functions $f_1$ and $f_2$
Trajectory for $f_2$
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