On smoothness of solutions to projected differential equations

David Salas; Lionel Thibault; Emilio Vilches

doi:10.3934/dcds.2019095

Article Contents

2019, Volume 39, Issue 4: 2255-2283. Doi: 10.3934/dcds.2019095

This issue Previous Article Construction solutions for Neumann problem with Hénon term in

$ \mathbb{R}^2 $

Next Article Prescribing the

$ Q' $

-curvature in three dimension

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
^* Corresponding author: David Salas

Received: August 2018

Revised: October 2018

Published online: April 2019

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 49J53, 34A60; Secondary: 49N60, 47J35, 37N40.

Citation:

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Figure 1. Two prox-regular sets with smooth and non-smooth boundary

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Figure 2. Sets of Definition 4.1 for a trajectory in $ \mathbb{R} ^2 $

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Figure 3. A circuit with an ideal diode, an inductor and a current source

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Figure 4. Functions $ f_1 $ and $ f_2 $

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Figure 5. Trajectory for $ f_2 $

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