Publications

• Article dans une revue

A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system

Emmanuel Creusé, Serge Nicaise, Roberta Tittarelli

In this paper, a guaranteed equilibrated error estimator is proposed for the harmonic magnetodynamic formulation of the Maxwell's system. This system is recast in two classical potential formulations, which are solved by a Finite Element method. The equilibrated estimator is built starting…

IMA Journal of Numerical Analysis, 2017, 37 (2), pp.750-773. ⟨10.1093/imanum/drw026⟩. ⟨hal-01110258⟩

• Article dans une revue

Null pseudo-isotropic Lagrangian surfaces

A Carriazo, V. Martin-Molina, Luc Vrancken

We show that a Lagrangian, Lorentzian surface M? in a complex space form (M) over tilde (2)(1) (4c) is pseudo-isotropic if and only if M is minimal. Next we obtain a complete classification of all Lagrangian, Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isotropic.

Colloquium Mathematicum, 2017, 150 (1), pp.87-101. ⟨10.4064/cm7107s-12-2016⟩. ⟨hal-03233891⟩

• Article dans une revue

Regularity of solutions of elliptic problems with a curved fracture

S. Ariche, Colette De Coster, Serge Nicaise

We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof…

Journal of Mathematical Analysis and Applications, 2017, 447 (2), pp.908-932. ⟨10.1016/j.jmaa.2016.10.021⟩. ⟨hal-03149894⟩

• Article dans une revue

A penalty method for a linear Koiter shell model

Ismail Merabet, Serge Nicaise

In this paper a penalized method and its approximation by finite element method are proposed to solve Koiter's equations for a thin linearly elastic shell. In addition to existence and uniqueness results of solutions of the continuous and the discrete problems we derive some a priori error…

ESAIM: Mathematical Modelling and Numerical Analysis, 2017, 51 (5), pp.1783-1803. ⟨10.1051/m2an/2017009⟩. ⟨hal-01956616⟩

• Article dans une revue

Control and stabilization of 2 × 2 hyperbolic systems on graphs

Serge Nicaise

We consider 2 × 2 (first order) hyperbolic systems on networks subject to general transmission conditions and to some dissipative boundary conditions on some external vertices. We find sufficient but natural conditions on these transmission conditions that guarantee the exponential decay of the…

Mathematical Control and Related Fields, 2017, 7 (1), pp.53-72. ⟨10.3934/mcrf.2017004⟩. ⟨hal-03152022⟩

• Chapitre d'ouvrage

A Note on the Asymptotic Stability of Wave-Type Equations with Switching Time-Delay

Serge Nicaise, Cristina Pignotti

We consider second-order evolution equations with intermittently delayed/not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, completing our previous results from Nicaise and Pignotti [Adv. Diff. Eq., 17: 879–902, 2012; J. Dyn. Diff. Eq., 26: 781–803, 2014].…

Kais Ammari; Stephane Gerbi. Evolution Equations: Long Time Behavior and Control, 1, Cambridge University Press, pp.137-150, 2017, 9781108412308. ⟨10.1017/9781108304023.007⟩. ⟨hal-03142598⟩

• Pré-publication, Document de travail

Cohomologie de Dolbeault feuilletée du feuilletage complexe affine de Reeb

Aziz El Kacimi Alaoui, Rochdi Ben Charrada

2017. ⟨hal-03165346⟩

• Article dans une revue

Optimal control of some quasilinear Maxwell equations of parabolic type

Serge Nicaise, Fredi Tröltzsch

An optimal control problem is studied for a quasilinear Maxwell equation of nondegenerate parabolic type. Well-posedness of the quasilinear state equation, existence of an optimal control, and weak Gateaux-differentiability of the control-to-state mapping are proved. Based on these results, first-…

Discrete and Continuous Dynamical Systems - Series S, 2017, 10 (6), pp.1375-1391. ⟨10.3934/dcdss.2017073⟩. ⟨hal-03166140⟩

• Article dans une revue

Control of the γ-alumina to α-alumina phase transformation for an optimized alumina densification

Samir Lamouri, M. Hamidouche, Noureddine Bouaouadja, H. Belhouchet, Vincent Garnier, Gilbert Fantozzi, Jean-François Trelcat

In this work, we studied the aptitude to sintering green bodies using γ-Al2O3 transition alumina as raw powder. We focused on the influence of the heating rate on densification and microstructural evolution. Phase transformations from transition alumina γ → δ → θ → α-Al2O3 were studied by in situ X…

Boletín de la Sociedad Española de Cerámica y Vidrio, 2017, 56 (2), pp.47-54. ⟨10.1016/j.bsecv.2016.10.001⟩. ⟨hal-01804220⟩

• Article dans une revue

Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map.

B. Bektas, J. van Der Veken, Luc Vrancken

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are…

Ann. Global Anal. Geom., 2017, 52, pp.45-55. ⟨10.1007/s10455-017-9548-2⟩. ⟨hal-03233877⟩