June 2018, 13(2): 373-378. doi: 10.3934/nhm.2018016

Corrigendum to "(Almost) everything you always wanted to know about deterministic control problems in stratified domains"

Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François-Rabelais Tours, Parc de Grandmont, 37200 Tours, France

Received  September 2017 Revised  October 2017 Published  May 2018

Fund Project: This work was partially supported by the ANR HJnet ANR-12-BS01-0008-01 and by EU under the 7th Framework Programme Marie Curie Initial Training Network "FP7-PEOPLE-2010-ITN", SADCO project, GA number 264735-SADCO

The aim of this short note is: $(i)$ to report an error in [1]; $(ii)$ to explain why the comparison result of [1] lacks an hypothesis in the definition of subsolutions if we allow them to be discontinuous; $(iii)$ to describe a simple counter-example; $(iv)$ to show a simple way to correct this mistake, considering the classical Ishii's definition of viscosity solutions; $(v)$ finally, to prove that this modification actually fixes the the comparison and stability results of [1].

Citation: Guy Barles, Emmanuel Chasseigne. Corrigendum to "(Almost) everything you always wanted to know about deterministic control problems in stratified domains". Networks & Heterogeneous Media, 2018, 13 (2) : 373-378. doi: 10.3934/nhm.2018016
References:
[1]

G. Barles and E. Chasseigne, (Almost) Everything you always wanted to know about deterministic control problems in stratified domains, Netw. Heterog. Media, 10 (2015), 809-836. doi: 10.3934/nhm.2015.10.809.

[2]

A. Bressan and Y. Hong, Optimal control problems on stratified domains, Netw. Heterog. Media., 2 (2007), 313-331 (electronic) and Errata corrige: Optimal control problems on stratified domains. Netw. Heterog. Media., 8 (2013), p625. doi: 10.3934/nhm.2007.2.313.

show all references

References:
[1]

G. Barles and E. Chasseigne, (Almost) Everything you always wanted to know about deterministic control problems in stratified domains, Netw. Heterog. Media, 10 (2015), 809-836. doi: 10.3934/nhm.2015.10.809.

[2]

A. Bressan and Y. Hong, Optimal control problems on stratified domains, Netw. Heterog. Media., 2 (2007), 313-331 (electronic) and Errata corrige: Optimal control problems on stratified domains. Netw. Heterog. Media., 8 (2013), p625. doi: 10.3934/nhm.2007.2.313.

[1]

Steven Richardson, Song Wang. The viscosity approximation to the Hamilton-Jacobi-Bellman equation in optimal feedback control: Upper bounds for extended domains. Journal of Industrial & Management Optimization, 2010, 6 (1) : 161-175. doi: 10.3934/jimo.2010.6.161

[2]

Alberto Bressan, Yunho Hong. Optimal control problems on stratified domains. Networks & Heterogeneous Media, 2007, 2 (2) : 313-331. doi: 10.3934/nhm.2007.2.313

[3]

Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521

[4]

Guy Barles, Emmanuel Chasseigne. (Almost) Everything you always wanted to know about deterministic control problems in stratified domains. Networks & Heterogeneous Media, 2015, 10 (4) : 809-836. doi: 10.3934/nhm.2015.10.809

[5]

Cristopher Hermosilla. Stratified discontinuous differential equations and sufficient conditions for robustness. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4415-4437. doi: 10.3934/dcds.2015.35.4415

[6]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1

[7]

B. M. Adams, H. T. Banks, Hee-Dae Kwon, Hien T. Tran. Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches. Mathematical Biosciences & Engineering, 2004, 1 (2) : 223-241. doi: 10.3934/mbe.2004.1.223

[8]

Roberta Ghezzi, Benedetto Piccoli. Optimal control of a multi-level dynamic model for biofuel production. Mathematical Control & Related Fields, 2017, 7 (2) : 235-257. doi: 10.3934/mcrf.2017008

[9]

Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 617-633. doi: 10.3934/nhm.2010.5.617

[10]

Jean-Claude Zambrini. On the geometry of the Hamilton-Jacobi-Bellman equation. Journal of Geometric Mechanics, 2009, 1 (3) : 369-387. doi: 10.3934/jgm.2009.1.369

[11]

Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017

[12]

Anya Désilles, Hélène Frankowska. Explicit construction of solutions to the Burgers equation with discontinuous initial-boundary conditions. Networks & Heterogeneous Media, 2013, 8 (3) : 727-744. doi: 10.3934/nhm.2013.8.727

[13]

Pierpaolo Soravia. Existence of absolute minimizers for noncoercive Hamiltonians and viscosity solutions of the Aronsson equation. Mathematical Control & Related Fields, 2012, 2 (4) : 399-427. doi: 10.3934/mcrf.2012.2.399

[14]

Jingyu Li, Chuangchuang Liang. Viscosity dominated limit of global solutions to a hyperbolic equation in MEMS. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 833-849. doi: 10.3934/dcds.2016.36.833

[15]

Konstantinos Chrysafinos, Efthimios N. Karatzas. Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1473-1506. doi: 10.3934/dcdsb.2012.17.1473

[16]

Tianliang Hou, Yanping Chen. Superconvergence for elliptic optimal control problems discretized by RT1 mixed finite elements and linear discontinuous elements. Journal of Industrial & Management Optimization, 2013, 9 (3) : 631-642. doi: 10.3934/jimo.2013.9.631

[17]

Fulvia Confortola, Elisa Mastrogiacomo. Optimal control for stochastic heat equation with memory. Evolution Equations & Control Theory, 2014, 3 (1) : 35-58. doi: 10.3934/eect.2014.3.35

[18]

Jitka Machalová, Horymír Netuka. Optimal control of system governed by the Gao beam equation. Conference Publications, 2015, 2015 (special) : 783-792. doi: 10.3934/proc.2015.0783

[19]

Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437

[20]

Enrique Fernández-Cara, Juan Límaco, Laurent Prouvée. Optimal control of a two-equation model of radiotherapy. Mathematical Control & Related Fields, 2018, 8 (1) : 117-133. doi: 10.3934/mcrf.2018005

2016 Impact Factor: 1.2

Metrics

  • PDF downloads (12)
  • HTML views (65)
  • Cited by (0)

Other articles
by authors

[Back to Top]