Articles

2015

Article dans des revues

Infinite horizon problems on stratifiable state-constraints sets
Cristopher Hermosilla, Hasnaa Zidani
Journal of Differential Equations, Elsevier, 2015, 258 (4), pp.1430-1460. <10.1016/j.jde.2014.11.001>
https://hal.inria.fr/hal-00955921/file/Infinite_Horizon_Problems_on_Stratifiable_State_Constraints_sets.pdf BibTex
Optimal Design for Purcell Three-link Swimmer
Laetitia Giraldi, Pierre Martinon, Marta Zoppello
Physical Review, American Physical Society (APS), 2015, 91 (2), pp.023012
https://hal.archives-ouvertes.fr/hal-01098501/file/GMZ_rev2.pdf BibTex
A General Optimal Multiple Stopping Problem with an Application to Swing Options
Imene Ben Latifa, Joseph Frédéric Bonnans, Mohamed Mnif
Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2015, 33, pp.25. <10.1080/07362994.2015.1037592>
https://hal.inria.fr/hal-01248283/file/A_general_optimal_multiple_stopping_problem_with_an_application_to_Swing_Options_final.pdf BibTex
Zubov’s equation for state-constrained perturbed nonlinear systems
Lars Grüne, Hasnaa Zidani
Mathematical Control and Related Fields, AIMS, 2015, 5 (1), pp.55-71. <10.3934/mcrf.2015.5.55>
https://hal.inria.fr/hal-00931028/file/Zubov_obstacle_submitted.PDF BibTex
Numerical methods for an optimal multiple stopping problem
Imène Ben Latifa, Joseph Fréderic Bonnans, Mohamed Mnif
Stochastics and Dynamics, World Scientific Publishing, 2015, 16 (4), pp.27. <10.1142/S0219493716500167>
https://hal.inria.fr/hal-01248282/file/Numerical_methods_for_an_optimal_multiple_stopping_problem_Jul_2015.pdf BibTex
Analysis of a periodic optimal control problem connected to microalgae anaerobic digestion
Térence Bayen, Francis Mairet, Pierre Martinon, Matthieu Sebbah
Optimal Control Applications and Methods, Wiley, 2015, pp.24. <10.1002/oca.2127>
https://hal.archives-ouvertes.fr/hal-00860570/file/BMMS-HAL.pdf BibTex
Mean field games systems of first order
Pierre Cardaliaguet, Philip Jameson Graber
ESAIM – Control Optimisation and Calculus of Variations, EDP Sciences, 2015, 21 (3), pp.690-722
https://hal.archives-ouvertes.fr/hal-00925905/file/mean_field_games-20140108.pdf BibTex
Dynamic Programming and Error Estimates for Stochastic Control Problems with Maximum Cost
Olivier Bokanowski, Athena Picarelli, Hasnaa Zidani
Applied Mathematics and Optimization, Springer Verlag (Germany), 2015, 71 (1), pp.125–163. <10.1007/s00245-014-9255-3>
https://hal.inria.fr/hal-00931025/file/Bokanowski_Picarelli_Zidani_revised.pdf BibTex
Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations
Axel Kröner, Sergio S. Rodrigues
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1020-1055
https://hal.archives-ouvertes.fr/hal-01089893/file/Kroener_Rodrigues_2015.pdf BibTex
Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance
Bernard Bonnard, Mathieu Claeys, Olivier Cots, Pierre Martinon
Acta Applicandae Mathematicae, Springer Verlag, 2015, 135 (1), pp.5-45. <10.1007/s10440-014-9947-3>
https://hal.inria.fr/hal-00867753/file/art.pdf BibTex
Monotone numerical schemes and feedback construction for hybrid control systems
Roberto Ferretti, Hasnaa Zidani
Journal of Optimization Theory and Applications, Springer Verlag, 2015, 165 (2), pp.507-531. <10.1007/s10957-014-0637-0>
https://hal.inria.fr/hal-00989492/file/Ferretti-Zidani_Hal-V2.pdf BibTex
Second order mean field games with degenerate diffusion and local coupling
Pierre Cardaliaguet, J. Graber, Alessio Porretta, Daniela Tonon
NoDEA. Nonlinear Differential Equations and Applications, 2015, 22 (5), pp.1287-1317
https://hal.archives-ouvertes.fr/hal-01049834/file/cptg20140722.pdf BibTex

2014

Article dans des revues

Singular perturbation of optimal control problems on multi-domains
Nicolas Forcadel, Zhiping Rao
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (5), pp.2917-2943. <10.1137/130916709>
https://hal.archives-ouvertes.fr/hal-00812846/file/FR110413.pdf BibTex
Getting the most out of it: optimal experiments for parameter estimation of microalgae growth models
Rafael Muñoz-Tamayo, Pierre Martinon, Gaël Bougaran, Francis Mairet, Olivier Bernard
Journal of Process Control, Elsevier, 2014, 24 (6), pp.991-1001. <http://www.sciencedirect.com/science/article/pii/S095915241400122X>. <10.1016/j.jprocont.2014.04.021>
https://hal.inria.fr/hal-00998525/file/Munoz%20OED_vfinal.pdf BibTex
Second-order sufficient conditions for strong solutions to optimal control problems
Joseph Frederic Bonnans, Xavier Dupuis, Laurent Pfeiffer
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2014, 20 (03), pp.704-724. <10.1051/cocv/2013080>
https://hal.inria.fr/hal-00825260/file/RR-8307.pdf BibTex
Optimization of running strategies based on anaerobic energy and variations of velocity
Amandine Aftalion, J. Frederic Bonnans
SIAM Journal of Applied Mathematics, 2014, 74 (5), pp.1615-1636
https://hal.inria.fr/hal-00851182/file/runFinal.pdf BibTex
Optimal control of a semilinear parabolic equation with singular arcs
Joseph Frederic Bonnans
Optimization, Methods and Software, Taylor and Francis, 2014, 29 (2), pp.964-978. <10.1080/10556788.2013.830220>
https://hal.inria.fr/hal-00740698/file/heatsingularHALrevision.pdf BibTex
Sensitivity analysis for the outages of nuclear power plants
Kengy Barty, J. Frederic Bonnans, Laurent Pfeiffer
Energy Systems, Springer, 2014, 5 (2), pp.371-406. <10.1007/s12667-013-0096-y>
https://hal.inria.fr/hal-00671186/file/RR-7884.pdf BibTex
Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations
Térence Bayen, J. Frederic Bonnans, Francisco J. Silva
Transactions American Mathematical Society, American Mathematical Society, 2014, 366 (4), pp.2063–2087. <10.1090/S0002-9947-2013-05961-2>
https://hal.inria.fr/inria-00632308/file/tbfbfstams-2HAL.pdf BibTex
A minimum effort optimal control problem for the wave equation.
Axel Kröner, Karl Kunisch
Computational Optimization and Applications, Springer Verlag, 2014, 57 (1), pp.241-270
https://hal.archives-ouvertes.fr/hal-01089336/file/kroenerkunisch2013.pdf BibTex
Level-set approach for Reachability Analysis of Hybrid Systems under Lag Constraints
Giovanni Granato, Hasnaa Zidani
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.606–628. <10.1137/120874205>
https://hal.inria.fr/hal-00735724/file/Granato-Zidani.pdf BibTex
Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations
Zhiping Rao, Antonio Siconolfi, Hasnaa Zidani
Journal of Differential Equations, Elsevier, 2014, 257 (11), pp.3978–4014. <10.1016/j.jde.2014.07.015>
https://hal.inria.fr/hal-00820273/file/Rao-Siconolfi-Zidani2013.pdf BibTex
Optimal feedback control of undamped wave equations by solving a HJB equation
Axel Kröner, Karl Kunisch, Hasnaa Zidani
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2014, 21 (2), pp.442 – 464. <10.1051/cocv/2014033>
https://hal.archives-ouvertes.fr/hal-00924089/file/KroenerKunischZidani2013v1.pdf BibTex
Second-order necessary conditions in Pontryagin form for optimal control problems
J. Frederic Bonnans, Xavier Dupuis, Laurent Pfeiffer
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3887-3916. <10.1137/130923452>
https://hal.inria.fr/hal-00825273/file/RR-8306.pdf BibTex
Optimal control of leukemic cell population dynamics
Xavier Dupuis
Mathematical Modeling for Natural Phenomena, 2014, Issue dedicated to Michael Mackey, 9 (1), pp.4-26. <10.1051/mmnp/20149102>
https://hal.inria.fr/hal-00858208/file/RR-8356.pdf BibTex

2013

Article dans des revues

A discontinuous Galerkin scheme for front propagation with obstacles
Olivier Bokanowski, Yingda Cheng, Chi-Wang Shu
Numerische Mathematik, Springer Verlag, 2013, 126 (1), pp.1-31. <10.1007/s00211-013-0555-3>
https://hal.inria.fr/hal-00653532/file/main.pdf BibTex
A model-free no-arbitrage price bound for variance options
J. Frederic Bonnans, Xiaolu Tan
Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68 (1), pp.43-73. <10.1007/s00245-013-9197-1>
https://hal.inria.fr/inria-00634387/file/RR-7777.pdf BibTex
Sensitivity analysis for relaxed optimal control problems with final-state constraints
Joseph Frederic Bonnans, Laurent Pfeiffer, Oana Silvia Serea
Nonlinear Analysis: Theory, Methods & Applications, Elsevier, 2013, 89, pp.55-80. <10.1016/j.na.2013.04.013>
https://hal.inria.fr/hal-00702246/file/RR-7977.pdf BibTex
A Shooting Algorithm for Optimal Control Problems with Singular Arcs
Maria Soledad Aronna, J. Frederic Bonnans, Pierre Martinon
Journal of Optimization Theory and Applications, Springer Verlag, 2013, 158 (2), pp.419-459. <10.1007/s10957-012-0254-8>
https://hal.inria.fr/inria-00631332/file/RR-7763.pdf BibTex
A general Hamilton-Jacobi framework for nonlinear state-constrained control problems
Albert Altarovici, Olivier Bokanowski, Hasnaa Zidani
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2013, 19 (2), pp.337–357. <10.1051/cocv/2012011>
https://hal.inria.fr/hal-00653337/file/MAIN_Hal.pdf BibTex
A Hamilton-Jacobi approach to junction problems and application to traffic flows
Cyril Imbert, Régis Monneau, Hasnaa Zidani
ESAIM – ESAIM – Control Optimisation and Calculus of Variations, COCV, 2013, 19 (01), pp 129-166. <10.1051/cocv/2012002>
https://hal.archives-ouvertes.fr/hal-00569010/file/jonction-hal3.pdf BibTex
An adaptive sparse grid semi-lagrangian scheme for first order Hamilton-Jacobi Bellman equations
Olivier Bokanowski, Jochen Garcke, Michael Griebel, Irene Klompmaker
Journal of Scientific Computing, Springer Verlag, 2013, 55, pp. 575-605. <10.1007/s10915-012-9648-x>
https://hal.archives-ouvertes.fr/hal-00741178/file/Bokanowski_Garcke_Griebel_Klompmaker_jsc.pdf BibTex
State-constrained Optimal Control Problems of Impulsive Differential Equations
Nicolas Forcadel, Zhiping Rao, Hasnaa Zidani
Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68, pp.1–19. <10.1007/s00245-013-9193-5>
https://hal.inria.fr/hal-00653671/file/Article_BRZ.pdf BibTex
First and second order optimality conditions for optimal control problems of state constrained integral equations
J. Frédéric Bonnans, Constanza De La Vega, Xavier Dupuis
Journal of Optimization Theory and Applications, Springer Verlag, 2013, 159 (1), pp.1-40. <10.1007/s10957-013-0299-3>
https://hal.inria.fr/hal-00697504/file/RR-7961.pdf BibTex

2012

Article dans des revues

First and second order necessary conditions for stochastic optimal control problems
Joseph Frédéric Bonnans, Francisco Silva
Applied Mathematics and Optimization, Springer Verlag (Germany), 2012, 65 (3), pp.403-439
https://hal.inria.fr/inria-00537227/file/versioninria2.pdf BibTex
Characterization of a local quadratic growth of the Hamiltonian for control constrained optimal control problems
J. Frédéric Bonnans, Nikolai Osmolovskii
Dynamics of Continuous, Discrete and Impulsive Systems, Waterloo Press, 2012, 19 (1-2), pp.1-16
https://hal.inria.fr/inria-00577604/file/RR-7570.pdf BibTex
Quadratic conditions for bang-singular extremals
Maria Soledad Aronna, J. Frederic Bonnans, Andrei V. Dmitruk, Pablo Lotito
Numerical Algebra, Control and Optimization, AIMS Journal, American Institute for Mathematical Sciences, 2012, A special issue dedicated to Professor Helmut Maurer on the occasion of his 65th. birthday, 2 (3), pp.511-546. <10.3934/naco.2012.2.511>
https://hal.inria.fr/inria-00605128/file/RR-7664.pdf BibTex
Asymptotic expansions for interior penalty solutions of control constrained linear-quadratic problems
Felipe Alvarez, Jérôme Bolte, J. Frederic Bonnans, Francisco Silva
Mathematical Programming, Series A, Springer, 2012, 135 (1-2), pp.473-507
https://hal.inria.fr/inria-00365540/file/RR-6863.pdf BibTex
Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate
Ariela Briani, Fabio Camilli, Hasnaa Zidani
Differential Equations and Applications, Ele-Math, 2012, 4, pp.297-317. <10.7153/dea-04-18>
https://hal.inria.fr/inria-00627520/file/briani_camilli_zidani_finalversion.pdf BibTex
A Patchy Dynamic Programming Scheme for a Class of Hamilton-Jacobi-Bellman Equations
Simone Cacace, Emiliano Cristiani, Maurizio Falcone, Athena Picarelli
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (5), pp.A2625-A2649. <10.1137/110841576>
https://hal.inria.fr/inria-00628108/file/CacaceChristianiFalconePicarelli_2011.pdf BibTex
Error estimates for the logarithmic barrier method in stochastic linear quadratic optimal control problems
Joseph Frédéric Bonnans, Francisco Silva
Systems and Control Letters, Elsevier, 2012, 61 (1), pp.143-147
https://hal.inria.fr/inria-00537229/file/RR-7455.pdf BibTex

2011

Article dans des revues

Asymptotic expansions for interior solutions of semilinear elliptic problems
J. Frederic Bonnans, Francisco Silva
SIAM J. Control Optim., SIAM, 2011, 49 (6), pp.2494-2517
https://hal.inria.fr/inria-00436768/file/RR-7126.pdf BibTex
Application of convex lexicographical optimization to the balance of GRTgaz gas grid
Joseph Frederic Bonnans, Ruben Paraisy, Sébastien Veyrat, Soizic Adam
Journal of Global Optimization, Springer Verlag, 2011, 49 (3), pp.415–423
BibTex
Optimal Control of the Atmospheric Reentry of a Space Shuttle by an Homotopy Method
Audrey Hermant
Optimal Control Applications and Methods, Wiley, 2011, 32 (6), pp.627-646. <10.1002/oca.961>
https://hal.inria.fr/inria-00317722/file/RR-6627.pdf BibTex
Characterization of the value function of final state constrained control problems with BV trajectories
Ariela Briani, Hasnaa Zidani
Communications on Pure and Applied Mathematics, Wiley, 2011, 10 (6), pp.1567-1587. <10.3934/cpaa.2011.10.1567>
https://hal.inria.fr/inria-00627518/file/Briani-Zidani.pdf BibTex
A discontinuous Galerkin solver for front propagation
Olivier Bokanowski, Yingda Cheng, Chi-Wang Shu
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2011, 33 (2), pp.923-938
https://hal.inria.fr/hal-00653471/file/Bokanowski_Cheng_Shu_2011.pdf BibTex
Optimal structure of gas transmission trunklines
J. Frederic Bonnans, Jean André
Optimization and Engineering, Springer Verlag, 2011, 12 (1), pp.175-198
https://hal.inria.fr/inria-00350522/file/RR-6791.pdf BibTex
Deterministic state constrained optimal control problems without controllability assumptions
Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2011, 17 (4), pp. 995-1015. <10.1051/cocv/2010030>
https://hal.archives-ouvertes.fr/hal-00415953/file/BFZ-caracterisationV.pdf BibTex
Energy contracts management by stochastic programming techniques
Zhihao Cen, J. Frederic Bonnans, Thibault Christel
Annals of Operations Research, Springer Verlag, 2011, 200 (1), pp.199-222. <10.1007/s10479-011-0973-5>
https://hal.inria.fr/inria-00486897/file/RR-7289.pdf BibTex

2010

Article dans des revues

Optimal control of state constrained integral equations
J. Frederic Bonnans, Constanza De La Vega
Set-Valued and variational analysis, Springer, 2010, 18 (3), pp.307-326
https://hal.inria.fr/inria-00473952/file/RR-7257.pdf BibTex
Quadratic growth conditions in optimal control problems
Joseph Frederic Bonnans, Nikolai Osmolovskii
CONTEMPORARY MATHEMATICS SERIES, American Mathematical Society, 2010, Nonlinear Analysis and Optimization II: Optimization, 514, pp.85–98
BibTex
Lipschitz solutions of optimal control problems with state constraints of arbitrary order
J. Frederic Bonnans
Mathematics and its Applications / Annals of AOSR, AOSR, 2010, 2 (1), pp.78-98
https://hal.inria.fr/inria-00465660/file/RR-7229.pdf BibTex
L^1-error estimate for numerical approximations of Hamilton-Jacobi-Bellman equations in dimension 1.
Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani
Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2010, 79 (271), pp.1395–1426
https://hal.inria.fr/inria-00267644/file/Artticle.pdf BibTex
An efficient data structure to solve front propagation problems
Olivier Bokanowski, Emiliano Cristiani, Hasnaa Zidani
Journal of Scientific Computing, Springer Verlag, 2010, 42 (2), pp.251–273. <10.1007/s10915-009-9329-6>
https://hal.inria.fr/inria-00273977/file/Bok-Cri-Zid.pdf BibTex
Second-order analysis of optimal control problems with control and initial-final state constraints
J. Frederic Bonnans, Nikolai Osmolovskii
J. Convex Analysis, Heldermann, 2010, 17 (3), pp.885-913
https://hal.inria.fr/inria-00335869/file/RR-6707.pdf BibTex
Convergence of a non-monotone scheme for Hamilton-Jacobi-Bellman equations with discontinuous data
Olivier Bokanowski, Nadia Megdich, Hasnaa Zidani
Numerische Mathematik, Springer Verlag, 2010, 115 (1), pp.1–44. <10.1007/s00211-009-0271-1>
https://hal.inria.fr/inria-00193157/file/Zidani-main.pdf BibTex
Reachability and minimal times for state constrained nonlinear problems without any controllability assumption
Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (7), pp. 4292-4316
https://hal.archives-ouvertes.fr/hal-00395589/file/BFZ-Obstacle.pdf BibTex
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
Audrey Hermant
Applied Mathematics and Optimization, Springer Verlag (Germany), 2010, 61 (1), pp.85-127. <10.1007/s00245-009-9076-y>
https://hal.inria.fr/inria-00316281/file/RR-6626.pdf BibTex
Optimal control of a parabolic equation with time-dependent state constraints
J. Frederic Bonnans, Pascal Jaisson
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (7), pp.4550-4571
https://hal.inria.fr/inria-00348854/file/RR-6784.pdf BibTex
Explicit polyhedral approximation of the Euclidean ball
J. Frederic Bonnans, M. Lebelle
RAIRO-RO, EDP Sciences, 2010, 44 (1), pp.45-60
BibTex
Initialization of the shooting method via the Hamilton-Jacobi-Bellman approach
Emiliano Cristiani, Pierre Martinon
Journal of Optimization Theory and Applications, Springer Verlag, 2010, 146 (2), pp.321-346. <10.1007/s10957-010-9649-6>
https://hal.inria.fr/inria-00439543/file/RR-7139.pdf BibTex

2009

Article dans des revues

Second-order Analysis for Optimal Control Problems with Pure State Constraints and Mixed Control-State Constraints
Joseph Frederic Bonnans, Audrey Hermant
Annales de l’I.H.P. – Nonlinear Analysis, Elsevier, 2009, 26 (2), pp.561-598
BibTex
Revisiting the Analysis of Optimal Control Problems with Several State Constraints
Joseph Frederic Bonnans, Audrey Hermant
Control and Cybernetics, Polish Academy of Sciences, 2009, 38 (4), pp.1021–1052
BibTex
Planning reinforcement on gas transportation networks with optimization methods
Joseph Frederic Bonnans, Jean André, Laurent Cornibert
European Journal of Operational Research, Elsevier, 2009, 197 (3), pp.1019-1027
BibTex
Comparison principle for a Generalized Fast Marching Method
Nicolas Forcadel
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (3), pp. 1923-1951
https://hal.archives-ouvertes.fr/hal-00266075/file/monotoneGFMM.pdf BibTex
Homogenization of fully overdamped Frenkel-Kontorova models
Nicolas Forcadel, Cyril Imbert, Régis Monneau
Journal of Differential Equations, Elsevier, 2009, 246, pp 1057–1097. <10.1016/j.jde.2008.06.034>
https://hal.archives-ouvertes.fr/hal-00266994/file/fim2-170208.pdf BibTex
Control problems with mixed constraints and application to an optimal investment problem
J. Frederic Bonnans, Dan Tiba
Mathematical Reports, Romanian Academy of Sciences, 2009, 4, pp.293-306
BibTex
Numerical approximation for a superreplication problem under gamma constraints
Benjamin Bruder, Olivier Bokanowski, Stefania Maroso, Hasnaa Zidani
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 3 (47), pp.2289-2320
https://hal.archives-ouvertes.fr/hal-00278077/file/main.pdf BibTex
Some convergence results for Howard’s algorithm
Olivier Bokanowski, Stefania Maroso, Hasnaa Zidani
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2009, 47 (4), pp.3001–3026
https://hal.inria.fr/inria-00179549/file/RR-zidani.pdf BibTex
Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher
Pierre Martinon, J. Frederic Bonnans, Julien Laurent-Varin, Emmanuel Trélat
Journal of Guidance, Control, and Dynamics, American Institute of Aeronautics and Astronautics, 2009, 32 (1), pp.51–55
https://hal.archives-ouvertes.fr/hal-00312012/file/ariane5.pdf BibTex
Stability Analysis of Optimal Control Problems with a Second-order State Constraint
Audrey Hermant
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2009, 20 (1), pp.104-129. <10.1137/070707993>
https://hal.inria.fr/inria-00186968/file/secondorder-rr.pdf BibTex
Existence of solutions for a model describing the dynamics of junctions between dislocations
Nicolas Forcadel, Régis Monneau
SIAM Journal on Mathematical Analysis / SIAM Journal of Mathematical Analysis, springer, 2009, 40 (6), pp. 2517-2535. <10.1137/070710925>