Arnaud Diego Münch

Professeur


In Preparation

- Explicit approximation of the solution to the viscous Burgers's equation with shock layers. Avec Youcef Amirat. Soumis.

- A non linear optimal control problem related to a road de-icing device: Analysis and Numerical experiments. Avec Jérôme Lemoine et Frédéric Bernardin. En révision.

- Inverse problems for linear parabolic equations using mixed formulations - Part 2 : Numerical Analysis and experiments.

Publications

Google Scholar list - Mathscinet list


  1. On the exact boundary controllability of semilinear wave equations,
    with Sue Claret and Jérôme Lemoine,
    SIAM J. Control and Optimization 62(4), 1953-1976 (2024).

  2. Identification of fog particle size distribution by a radiative transfer equation inversion,
    with Frédéric Bernardin and Ali Krayem,
    Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 317, April 2024, 108923.

  3. Global boundary null controllability of one dimensional semi-linear heat equation,
    with Kuntal Bhandari and Jérôme Lemoine,
    Discrete and Continuous Dynamical Systems Serie S, 17(7), 2251-2297 (2024).
    Special issue in honor of Philippe Destuynder.

  4. Constructive exact controls for semi-linear wave equations,
    with Arthur Bottois and Jérôme Lemoine,
    Annals of Mathematical Sciences and Applications, 8(3), 629-675 (2023).
    Special issue on recent trends in applied mathematics and scientific computing in memory of Roland Glowinski.

  5. Space-time finite element methods for control problems subject to the wave equation,
    with Erik Burman, Ali Feizmohammadi and Lauri Oksanen,
    ESAIM:COCV 29(41), 40pp (2023).

  6. Internal layer intersecting the boundary of a domain in a singular advection-diffusion equation,
    with Youcef Amirat,
    Asymptotic Analysis 134(3-4), 297-343 (2023).

  7. Exact boundary controllability of semilinear 1D wave equations through a constructive approach,
    with Kuntal Bhandari and Jérôme Lemoine,
    Mathematics of controls, signals and systems, 35(1), 77-123 (2023).

  8. Approximation of exact controls for semilinear wave and heat equations through space-time methods,
    Handbook of Numerical Analysis, Vol. XXIII Numerical control part B, Chapter 10, 341-376 (2023).

  9. Exact controllability of semilinear heat equations through a constructive approach,
    with Sylvain Ervedoza and Jérôme Lemoine,
    Evolution equations and control theory, 12(2), 567-599 (2023).

  10. Constructive exact control of semilinear 1D heat equations,
    with Jérôme Lemoine,
    Mathematical control and related fields 13(1), 382-414 (2023).

  11. Least-squares approaches for the 2D Navier-Stokes system,
    with Jérôme Lemoine,
    Radon Series on Computational and Applied Mathematics,
    Volume 29 "Optimization and Control for Partial Differential Equations", 285-342 (2022)

  12. Constructive exact control of semilinear 1D wave equations by a least-squares approach,
    with Emmanuel Trélat,
    SIAM J. Control and Optimization 60(2), 652-673 (2022).

  13. A fully space-time least-squares method for the unsteady Navier-Stokes system.
    with Jérôme Lemoine,
    Journal of Mathematical Fluid Mechanics 23(4), 102 (2021).

  14. Approximation of null controls for semilinear heat equations using a least-squares appproach,
    with Irene Marin-Gayte and Jérôme Lemoine,
    ESAIM:COCV 27(63), 28pp (2021).
    Special issue in honor of Enrique Zuazua on the occasion of his 60th birthday.

  15. Optimization of non cylindrical domains for the exact null controllability of the 1D wave equation,
    with Arthur Bottois and Nicolae Cindea,
    ESAIM:COCV 27(13), 32pp (2021).

  16. Space-time stabilized finite element methods for a unique continuation problem subject to the wave equation,
    with Erik Burman, Ali Feizmohammadi and Lauri Oksanen,
    ESAIM:M2AN 55, S969-S991 (2021).

  17. Analysis of continuous H^{-1} least-squares methods for the steady Navier-Stokes system,
    with Jérôme Lemoine and Pablo Pedregal,
    Applied Mathematics and Optimization 83(1), 461-488 (2021).

  18. Resolution of the Implicit Euler scheme for the Navier-Stokes equation through a least-squares method,
    with Jérôme Lemoine,
    Numerische Mathematik 147(2), 349-391 (2021).

  19. Singular asymptotic expansion of the exact control for the perturbed wave equation,
    with Carlos Castro,
    Asymptotic Analysis 122(1-2), 1-33 (2021).

  20. Asymptotic analysis of an advection-diffusion equation involving interacting boundary and internal layers,
    with Youcef Amirat,
    Mathematical Methods in the Applied Sciences 43, 6823-6860 (2020).

  21. Approximation of controls for the linear wave equation: a first order mixed formulation,
    with Santiago Montaner,
    Mathematical control and related fields 9(4), 729-758 (2019).

  22. Modeling and optimizing a road de-icing device by a nonlinear heating,
    with Frédéric Bernardin,
    ESAIM:M2AN 53(3), 775-803 (2019).

  23. On the controllability of an advection-diffusion with respect to the diffusion parameter: asymptotic analysis and numerical simulations,
    with Youcef Amirat,
    Dedicated to Philippe Ciarlet on the occasion of his 80th birthday. Special volume in Acta Mathematicae Applicatae Sinica, Englsih series, 35(1), 54-110 (2019).

  24. Asymptotic analysis of an advection-diffusion equation and application to boundary controllability,
    with Youcef Amirat,
    Asymptotic Analysis, 112(1-2), 59-106 (2019).

  25. Numerical estimations of the cost of boundary controls for the equation y_t- epsilon y_xx + M y_x=0 with respect to epsilon,
    SEMA SIMAI Springer Series (link) . Volume 17, 159-191 (2018)
    Recent Advances in PDEs: Analysis, Numerics and controls, in honor of Prof. Enrique Fernández-Cara's 60 birthday.

  26. About least-squares type approach to address direct and controllability problems,
    with Pablo Pedregal,
    London Mathematical Society Lecture Note Series 439, 118-136 (2017) (link).

  27. Best decay rate, observability and open-loop admissibility costs: discussions and numerical study,
    with Kais Ammari,
    Journal of Dynamics and Differential equations, 29(2), 385-407 (2017).

  28. Inverse problems for linear parabolic equations using mixed formulations - Part 1 : Theoretical analysis, (link),
    with Diego Araujo de Souza,
    Journal of Inverse and Ill posed problems, 25(4), 445-468 (2017).

  29. On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations,
    with Enrique Fernández-Cara and Diego Araujo de Souza,
    Journal of Scientific Computing, 70(2), 819-858 (2017).

  30. Simultaneous reconstruction of the solution and the source of hyperbolic equations from boundary measurements: a robust numerical approach,
    with Nicolae Cîndea,
    Inverse Problems, 32(11) 115020 (2016).

  31. Robust optimal Robin boundary control for the transient heat equation with random input data,
    with Jesus Martinez-Frutos, Mathieu Kessler and Francisco Periago,
    International Journal for Numerical Methods in Engineering, 108, 116-135 (2016).

  32. A mixed formulation for the direct approximation of the control of minimal L^2-weighted norm for the linear heat equation,
    with Diego Araujo de Souza,
    Advances in Computational Mathematics, 42(1), 85-125 (2016).

  33. Inverse problem for linear hyperbolic equations using mixed formulations,
    with Nicolae Cîndea,
    Inverse Problems, 31(7), 075001 (2015).

  34. A mixed formulation for the direct approximation of the control of minimal L^2-norm for linear type wave equations,
    with Nicolae Cîndea,
    Calcolo, 52(03) 245-288 (2015).

  35. A least-squares formulation for the approximation of controls for the Stokes system.
    Mathematics of Control, Signals, and Systems, 27, 49-75 (2015).

  36. Controllability of the linear 1D-wave equation with inner moving forces,
    with Carlos Castro and Nicolae Cîndea,
    SIAM Control and Optimization, 52(06), 4027-4056 (2014).

  37. Numerical null controllability of the heat equation through a least squares and variational approach,
    with Pablo Pedregal,
    European Journal of Applied Mathematics, 25(03), 277-306 (2014).

  38. Numerical null controllability of the 1D heat equation: Duality and Carleman weights,
    with Enrique Fernández-Cara,
    J. Optimization, Theory and Applications, 163(01), 253-285 (2014).

  39. A least-squares formulation for the approximation of null controls for the Stokes system,
    with Pablo Pedregal,
    C.R. Acad. Sci. Paris, Série. I, 351, 545-550 (2013).

  40. Numerical approximation of bang-bang controls for the heat equation: an optimal design approach,
    with Francisco Periago,
    Systems and Control letters, 62, 643-655 (2013).

  41. Numerical controllability of the wave equation through primal methods and Carleman estimates,
    with Nicolae Cîndea and E. Fernández-Cara,
    ESAIM:COCV, 19(4), 1076-1108 (2013).

  42. A variational approach to approximate controls for system with essential spectrum: application to the membranal arch,
    Evolution Equations and Control Theory (AIMS), 2(1), 119-151 (2013).

  43. Strong convergent approximations of null controls for the heat equation,
    with Enrique Fernández-Cara,
    SeMA, 61(1), 49-78 (2013).

  44. Numerical null controllability of semi-linear 1D heat equations : fixed point, least squares and Newton methods,
    with Enrique Fernández-Cara,
    Mathematical Control and Related Fields (AIMS), 3(2), 217-246 (2012).

  45. Numerical null controllability of a semi-linear 1D heat equation via a least squares reformulation,
    with Enrique Fernández-Cara,
    C.R. Acad. Sci. Paris, Série. I, 349, 867-871 (2011).

  46. Exact controllability of a system of mixed order with essential spectrum,
    with Farid Ammar-Khodja and Karine Mauffrey,
    SIAM Control and Optimization, 49, 1857-1879 (2011).

  47. Optimal distribution of the internal null control for the 1D heat equation,
    with Francisco Periago,
    J. Differential Equations, 250, 95-111 (2011).

  48. Long time behavior of a two-phase optimal design for the heat equation,
    with Grégoire Allaire and Francisco Periago,
    SIAM Control and Optimization, 48(8), 5333-5356 (2010).

  49. Numerical approximation of null controls for the heat equation : ill-posedness and remedies,
    with Enrique Zuazua,
    Inverse Problems, 26(8),085018 (2010).

  50. Null boundary controllability of a circular elastic arch,
    IMA Journal of Mathematical Control and Information, 27(2), 119-144 (2010).

  51. Exact controllability of a string submitted to a boundary unilateral constraint,
    with Farid Ammar-Khodja and Sorin Micu,
    Annales de l'Institut Henri Poincaré (C), 27(4), 1097-1119 (2010).

  52. Relaxation of an optimal design problem in fracture mechanic : the anti-plane case,
    with Pablo Pedregal ,
    Esaim:COCV, 16(3), 719-743 (2010).

  53. Optimal internal stabilization of the linear system of elasticity,
    with Pablo Pedregal and Francisco Periago,
    Archive for Rational Mechanics and Analysis, 193(1), 171-193 (2009).

  54. Uniformly controllable schemes for the wave equation on the unit square,
    with Mark Asch ,
    Journal Optimization Theory and Application, 143(3), 417-438 (2009).

  55. Optimal location of the support of the control for the 1-D wave equation : numerical investigations.
    Computational Optimization and Applications, 42, 443-470 (2009).

  56. Controllability of a piezoelectric body. Theory and numerical simulation,
    with Bernadette Miara,
    Applied Mathematics and Optimization, 59(3), 383-412 (2009).

  57. Optimal internal stabilization of a damped wave equation by a topological approach,
    Int. J. Applied Mathematics and Computer Science, 19(1), 15-37 (2009).

  58. On the active control of crack growth in elastic media,
    with Patrick Hild and Yves Ousset,
    Computer Methods in Applied Mechanics and Engineering, 198, 407-419 (2008).

  59. Boundary stabilization on a nonlinear arch : Theoretical vs. Numerical Analysis,
    with Ademir Fernando Pazoto,
    Discrete and Continuous Dynamical Systems, Series B, 10(1), 197-219 (2008).

  60. On the exact controllability of a system of mixed order with essential spectrum,
    with Farid Ammar-Khodja and Giuseppe Geymonat,
    C.R. Acad. Sci. Paris, Série I, 346 (11/12), 629-634 (2008).

  61. On the control of crack growth in elastic media,
    with Patrick Hild and Yves Ousset ,
    C.R.Acad.Sci. Paris, Série IIb, 336(5), 422-427 (2008).

  62. Relaxation of an optimal design problem for the heat equation,
    with Pablo Pedregal and Francisco Periago,
    Journal de Mathématiques Pures et Appliquées, 89(3), 225-247 (2008).

  63. Optimal design under the one-dimensional wave equation,
    with Faustino Maestre and Pablo Pedregal,
    Interface and Free Boundaries, 10(1), 87-117 (2008).

  64. Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square,
    with Carlos Castro and Sorin Micu,
    IMA Journal of Numerical Analysis, 28(1), 186-214 (2008).

  65. Optimal design of the support of the control for the 2-D wave equation : numerical investigations.
    International Journal of Numerical Analysis and Modeling, 5(2), 331-351 (2008).

  66. A spatio-temporal design problem for a damped wave equation,
    with Faustino Maestre and Pablo Pedregal,
    SIAM Journal on Applied Mathematics, 68(1), 109-132 (2007).

  67. Uniform stabilization of a viscous numerical approximation for a locally damped wave equation,
    with Ademir Fernando Pazoto,
    Esaim: Control, Optimisation and Calculus of Variations, 13(2), 265-293 (2007).

  68. Optimal design of the damping set for the stabilization of the wave equation,
    with Pablo Pedregal and Francisco Periago,
    Journal of Differential Equation, 231(1), 331-358 (2006).

  69. A shape optimal design problem related to the exact controllability of the 2-D wave equation,
    C.R.Acad. Sci. Paris Série I, 343(3), 213-218 (2006).

  70. A variational approach to a shape design problem for the wave equation,
    with Pablo Pedregal and Francisco Periago ,
    C.R.Acad. Sci. Paris Série I, 343(5), 371-376 (2006).

  71. A uniformly controllable and implicit scheme for the 1-D wave equation,
    Mathematical Modelling and numerical analysis, 39(2), 377-418 (2005).

  72. Asymptotic consideration shedding light on incompressible shell models,
    with Dominique Chapelle and Cristinel Mardaré ,
    J. of Elasticity, 76(3), 199-246 (2004).

  73. Family of implicit and controllable schemes for the 1-D wave equation,
    C.R.Acad. Sci. Paris Série I, 339(10), 733-738 (2004).

  74. Mathematical analysis of nonlinear bonded joints models,
    with Francoise Krasucki and Yves Ousset ,
    Math. Models Meth. Appli. Sci., 14(4), 535-556 (2004).

  75. Numerical simulation of debonding of adhesively bonded joints,
    with Francoise Krasucki and Yves Ousset ,
    Int. J. of Solids and Structures, 39(26), 6355-6383 (2002).

  76. Numerical simulation of delamination growth in curved interfaces,
    with Yves Ousset,
    Computer Methods in Applied Mechanics and Engineering, 191(19-20), 2073-2095 (2002).

  77. Asymptotic analysis of a bonded joint in nonlinear elasticity,
    with Francoise Krasucki and Yves Ousset,
    C.R.Acad. Sci. Paris Série IIb, 329, 429-434 (2001).

  78. Energy release rate for a thin curvilinear beam,
    with Yves Ousset,
    C.R.Acad. Sci. Paris Série IIb, 328, 471-476 (2000).


Thesis and Habilitation

- Three dimensional crack growth in layered composites media: curved interfaces and bonded joints, Thèse de doctorat, Paris VI (2002).

- Analyse numérique de quelques problèmes de contrôle et d'optimisation de forme pour des systèmes dynamiques, Habilitation à diriger des recherches - Université de Franche-Comté (2008) (Slides).