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Article dans une revue

Well-posedness and stability results for nonlinear abstract evolution equations with time delays

Serge Nicaise, Cristina Pignotti

We consider abstract evolution equations with a nonlinear term depending on the state and on delayed states. We show that, if the -semigroup describing the linear part of the model is exponentially stable, then the whole system retains this property under some Lipschitz continuity assumptions on…

Journal of Evolution Equations, 2018, 18 (2), pp.947-971. ⟨10.1007/s00028-018-0427-5⟩. ⟨hal-03166220⟩

Article dans une revue

A prescribed anisotropic mean curvature equation modeling the corneal shape: A paradigm of nonlinear analysis

Chiara Corsato, Colette De Coster, Franco Obersnel, Pierpaolo Omari, Alessandro Soranzo

In this paper we survey, complete and refine some recent results concerning the Dirichlet problem for the prescribed anisotropic mean curvature equation (Equation Presented), in a bounded Lipschitz domain Ω ⊂ RN, with a, b > 0 parameters. This equation appears in the description of the geometry…

Discrete and Continuous Dynamical Systems - Series S, 2018, 11 (2), pp.213-256. ⟨10.3934/dcdss.2018013⟩. ⟨hal-03135736⟩

Article dans une revue

Mechanical Properties, Structure, Bioactivity and Cytotoxicity of Bioactive Na-Ca-Si-P-O-(N) Glasses

Assia Mabrouk, Ahmed Bachar, Ali Atbir, Claudine Follet-Houttemane, Cyrille Albert-Mercier, Arnaud Tricoteaux, Anne Leriche, Stuart Hampshire

Bioactive glasses are able to bond to bone through formation of carbonated hydroxyapatite in body fluids. However, because of their poor strength their use is restricted to non-load-bearing applications. The effects of nitrogen addition on the physical and mechanical properties and structure of…

Journal of the mechanical behavior of biomedical materials, 2018, 86, pp.284-293. ⟨10.1016/j.jmbbm.2018.06.023⟩. ⟨hal-04351733⟩

Article dans une revue

Classification of δ(2,n − 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

Bang-Yen Chen, Franki Dillen, Joeri van Der Veken, Luc Vrancken

It was proven in [4] that every Lagrangian submanifold M of a complex space form M˜n(4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2,n−2)≤[Formula presented]H2+2(n−2)c, where H2 is the squared mean curvature and δ(2,n−2) is a δ-invariant on M. In…

Journal of Mathematical Analysis and Applications, 2018, 458 (2), pp.1456-1485. ⟨10.1016/j.jmaa.2017.10.044⟩. ⟨hal-03233923⟩

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Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics

Théophile Chaumont-Frelet, Serge Nicaise, David Pardo

We analyze the use of non-fitting meshes for simulating the propagation of electromagnetic waves inside the Earth. In order to take into account subcell conductivity variations, we propose a simple " exact integration technique " that avoids the use of parameter homogenization and employs…

SIAM Journal on Numerical Analysis, 2018, 56 (4), pp.2288-2321. ⟨10.1137/16m1105566⟩. ⟨hal-01706452v2⟩

Article dans une revue

Study of novel oxyfluoronitride bioglasses

Assia Mabrouk, A. Marrouche, Claudine Follet-Houttemane, Ali Atbir, L. Boukir, Fouad Bentiss, A. Bachar

Bioglasses are used as bone substitutes and prosthetic coatings. Following implantation, they are predisposed to generate a series of physicochemical reactions at the glass-bone interface. Bioglasses with molar composition: 55SiO2–8.5CaO–31.5Na2O–5CaF2 have been synthesized and characterized.…

Journal of Materials and Environmental Science , 2018, 9 (6), pp.1866-1874. ⟨hal-04351717⟩

Article dans une revue

Fast Spectral Galerkin Method for Logarithmic Singular Equations on a Segment

Carlos F. Jerez-Hanckes, Serge Nicaise, Carolina Urzúa-Torres

We present a fast Galerkin spectral method to solve logarithmic singular equations on segments. The proposed method uses weighted first-kind Chebyshev polynomials. Convergence rates of several orders are obtained for fractional Sobolev spaces H −1/2 (or H −1/2 00). Main tools are the approximation…

Journal of Computational Mathematics -International Edition-, 2018, 36 (1), pp.128-158. ⟨10.4208/jcm.1612-m2016-0495⟩. ⟨hal-01956620⟩

Article dans une revue

Influence of post-HIP temperature on microstructural and optical properties of pure MgAl2O4 spinel

Caroline Gajdowski, Judith Böhmler, Yannick Lorgouilloux, Sébastien Lemonnier, Sophie d'Astorg, Elodie Barraud, Anne Leriche

Transparent MgAl2O4 spinel ceramics were processed from sub-micrometric commercial powder by applying a two-step procedure: pressureless sintering under vacuum followed by hot isostatic pressing. To limit grain growth and to avoid secondary reactions or impurities, no additives or sintering aids…

Journal of the European Ceramic Society, 2017, 37 (16), pp.5347-5351. ⟨10.1016/j.jeurceramsoc.2017.07.031⟩. ⟨hal-03080454⟩

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 Δ 2 u + νu = −λΔu in D 1 , u = ∂ r u = 0 o n∂ D 1 , where D 1 is the unit ball in R N , is determined for ν < 0 as well as the nodal properties of the corresponding eigenfunctions. In particular, we show that the first eigenvalue…

Positivity, 2017, 21 (4), pp.1319-1340. ⟨10.1007/s11117-017-0469-x⟩. ⟨hal-01956618⟩

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 Gâteaux-different-iability 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-01956624⟩