## Arnaud Diego Münch

Professeur

### In Preparation

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

- Resolution of the Implicit Euler scheme for the Navier-Stokes equation through a least-squares method. Avec Jérôme Lemoine. Soumis.

- Asymptotic analysis of a transport-diffusion equations involving several boundary layers. Avec Youcef Amirat.

- A fully space-time least-squares method for the Navier-Stokes system. Avec Jérôme Lemoine.

- Exact controllabilty of the rayleigh beam equation: asymptotic analysis with respect to the thickness and boundary layers phenomenon. Avec Carlos Castro.

### Publications

Google Scholar list - Mathscinet list

1. Approximation of controls for the linear wave equation: a first order mixed formulation,
with Santiago Montaner,
To appear in Mathematical control and related fields.

2. Analysis of continuous H^{-1} least-squares methods for the steady Navier-Stokes system,
with Jérôme Lemoine and Pablo Pedregal,
To appear in Applied Mathematics and Optimization.

3. Modeling and optimizing a road de-icing device by a nonlinear heating,
with Frédéric Bernardin,
To appear in ESAIM:M2AN.

4. 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).

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

6. 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 Fernandez-Cara's 60 birthday.

with Pablo Pedregal,
London Mathematical Society Lecture Note Series 439, 118-136 (2017) (link).

8. 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).

9. 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).

10. 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).

11. 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).

12. 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).

13. 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).

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

15. 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).

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

17. 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).

18. 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).

19. 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).

20. 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).

21. 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).

22. 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).

23. 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).

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

25. 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).

26. 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).

27. 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).

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

29. 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).

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

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

32. 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).

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

34. 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).

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

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

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

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

39. 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).

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

41. 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).

42. 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).

43. 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).

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

45. 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).

46. 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).

47. 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).

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

49. 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).

50. 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).

51. 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).

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

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

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

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

56. 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).

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

58. 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).

59. 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).