Publicaciones

• Article dans une revue

Spectral analysis of a generalized buckling problem on a ball

Colette De Coster, Serge Nicaise, Christophe Troestler

In this paper, the spectrum of the following fourth order problem (Formula Presented.)where D1 is the unit ball in RN, is determined for ν< 0 as well as the nodal properties of the corresponding eigenfunctions. In particular, we show that the first eigenvalue is simple and that the corresponding...

Positivity, 2017, 21 (4), pp.1319-1340. ⟨10.1007/s11117-017-0469-x⟩. ⟨hal-03163589⟩

• 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

A mixed discontinuous finite element method for folded Naghdi's shell in Cartesian coordinates

Serge Nicaise, Ismail Merabet

In this work a mixed method and its DG formulation are proposed to solve Naghdi's equations for a thin linearly elastic shell. The unknowns of the problem are the displacement of the points of the middle surface, the rotation field of the normal vector to the middle surface of the shell and a...

Mathematics of Computation, 2017, 86 (303), pp.1-47. ⟨10.1090/mcom/3094⟩. ⟨hal-03159113⟩

• 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⟩

• 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⟩

• 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⟩