Introduction: On Enrique
ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. E3

Some of the main contributions of the highly cited mathematician Enrique Zuazua are outlined at the occasion of his sixtieth birthday. Through various anecdotes, it is shown that taking advantage of favourable chances is part of a fruitful career and can produce important results for the benefit of the whole community.

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DOI : 10.1051/cocv/2021092
Classification : 34L20, 35XXX, 49A22, 73K12, 74XXX, 93XXX
Keywords: Wave equations, stability, control theory, spectral analysis
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     title = {Introduction: {On} {Enrique}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Coron, Jean-Michel; Haraux, Alain. Introduction: On Enrique. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. E3. doi: 10.1051/cocv/2021092

[1] K. Beauchard and E. Zuazua, Large time asymptotics for partially dissipative hyperbolic systems. Arch. Ratl. Mech. Anal. 199 (2011) 177–227. | MR | Zbl | DOI

[2] C. Castro and E. Zuazua, Low frequency asymptotic analysis of a string with rapidly oscillating density. SIAM J. Appl. Math. 60 (2000) 1205–1233. | MR | Zbl | DOI

[3] T. Duyckaerts, X. Zhang and E. Zuazua, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials. Ann. Inst. Henri Poincaré Anal. Non Linéaire 25 (2008) 1–41. | MR | Zbl | Numdam | DOI

[4] S. Ervedoza, A. Marica and E. Zuazua, Numerical meshes ensuring uniform observability of one-dimensional waves: construction and analysis. IMA J. Numer. Anal. 36 (2016) 503–542. | MR | DOI

[5] C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 31–61. | MR | Zbl | DOI

[6] E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: the linear case. Adv. Differ. Equ. 5 (2000) 465–514. | MR | Zbl

[7] E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. Henri Poincaré Anal. Non Linéaire 17 (2000) 583–616. | MR | Zbl | Numdam | DOI

[8] R. Glowinski, C. H. Li and J.-L. Lions, A numerical approach to the exact boundary controllability of the wave equation. I. Dirichlet controls: description of the numerical methods. Jpn. J. Appl. Math. 7 (1990) 1–76. | MR | Zbl | DOI

[9] A. Haraux, Semi-linear hyperbolic problems in bounded domains. Math. Rep. 3 (1987) i–xxiv and 1–281. | MR | Zbl

[10] A. Haraux and E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Arch. Ratl. Mech. Anal. 100 (1988) 191–206. | MR | Zbl | DOI

[11] A. Haraux and E. Zuazua, Super-solutions of eigenvalue problems and the oscillation properties of second order evolution equations. J. Differ. Equ. 74 (1988) 11–28. | MR | Zbl | DOI

[12] L. I. Ignat and E. Zuazua, Convergence of a two-grid algorithm for the control of the wave equation. J. Eur. Math. Soc. (JEMS) 11 (2009) 351–391. | MR | Zbl | DOI

[13] J. A. Infante and E. Zuazua, Boundary observability for the space semi-discretizations of the 1-D wave equation. ESAIM: M2AN 33 (1999) 407–438. | MR | Zbl | Numdam | DOI

[14] V. Komornik and E. Zuazua, A direct method for the boundary stabilization of the wave equation. J. Math. Pures Appl. 69 (1990) 33–54. | MR | Zbl

[15] G. Lebeau and E. Zuazua, Decay rates for the three-dimensional linear system of thermoelasticity. Arch. Ratl. Mech. Anal. 148 (1999) 179–231. | MR | Zbl | DOI

[16] A. López, X. Zhang and E. Zuazua, Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations. J. Math. Pures Appl. 79 (2000) 741–808. | MR | Zbl | DOI

[17] A. Marica and E. Zuazua, Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation. C. R. Math. Acad. Sci. Paris 348 (2010) 1087–1092. | MR | Zbl | DOI

[18] A. Marica and E. Zuazua, High frequency wave packets for the Schrödinger equation and its numerical approximations. C. R. Math.Acad. Sci. Paris 349 (2011) 105–110. | MR | Zbl | DOI

[19] A. Münch and E. Zuazua, Numerical approximation of null controls for the heat equation: ill-posedness and remedies. Inverse Probl. 26 (2010) 085018. | MR | Zbl | DOI

[20] M. Negreanu and E. Zuazua, Convergence of a multigrid method for the controllability of a 1-d wave equation. C. R. Math. Acad. Sci. Paris 338 (2004) 413–418. | MR | Zbl | DOI

[21] Y. Privat, E. Trélat and E. Zuazua, Optimal location of controllers for the one-dimensional wave equation. Ann. Inst. Henri Poincaré Anal. Non Linéaire 30 (2013) 1097–1126. | MR | Zbl | Numdam | DOI

[22] Y. Privat, E. Trélat and E. Zuazua, Optimal shape and location of sensors for parabolic equations with random initial data. Arch. Ratl. Mech. Anal. 216 (2015) 921–981. | MR | DOI

[23] Y. Privat, E. Trélat and E. Zuazua, Actuator design for parabolic distributed parameter systems with the moment method. SIAM J. Control Optim. 55 (2017) 1128–1152. | MR | DOI

[24] L. T. Tebou and E. Zuazua, Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation. Adv. Comput. Math. 26 (2007) 337–365. | MR | Zbl | DOI

[25] E. Trélat, C. Zhang and E. Zuazua, Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces. SIAM J. Control Optim. 56 (2018) 1222–1252. | MR | DOI

[26] E. Zuazua, Contrôlabilité exacte d’un modèle de plaques vibrantes en un temps arbitrairement petit. C. R. Acad. Sci. Paris Sér. I Math. 304 (1987) 173–176. | MR | Zbl

[27] E. Zuazua, Decay estimates for some semilinear damped hyperbolic problems. Asymptotic Anal. 1 (1988) 161–185.

[28] E. Zuazua, Exact controllability for semilinear wave equations in one space dimension. Ann. Inst. Henri Poincaré Anal. Non Linéaire 10 (1993) 109–129. | MR | Zbl | Numdam | DOI

[29] E. Zuazua, Boundary observability for the finite-difference space semi-discretizations of the 2-D wave equation in the square. J. Math. Pures Appl. (9) 78 (1999) 523–563. | MR | Zbl | DOI

[30] E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. | MR | Zbl | DOI

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