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Article dans une revue

Adapted Numerical Methods for the Poisson Equation with $L^2$ Boundary Data in NonConvex Domains

Thomas Apel, Serge Nicaise, Johannes Pfefferer

The very weak solution of the Poisson equation with L 2 boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the L 2 (Ω)-norm with order 1/2 in convex domains but has a reduced convergence order in nonconvex domains…

SIAM Journal on Numerical Analysis, 2017, 55 (4), pp.1937-1957. ⟨10.1137/16m1062077⟩. ⟨hal-01957588⟩

Article dans une revue

Generalized Yangians and their Poisson counterparts

Dimitri Gurevich, Pavel Saponov

By generalized Yangians, we mean Yangian-like algebras of two different classes. One class comprises the previously introduced so-called braided Yangians. Braided Yangians have properties similar to those of the reflection equation algebra. Generalized Yangians of the second class, RTT-type…

Theoretical and Mathematical Physics, 2017, 192 (3), pp.1243 - 1257. ⟨10.1134/S004057791709001X⟩. ⟨hal-03172948⟩

Article dans une revue

Dispersive effects for the Schrodinger equation on the tadpole graph

Felix Ali Mehmeti, Kaïs Ammari, Serge Nicaise

We consider the free Schrodinger group e(-itd2/dx2) on the tadpole graph R. We first show that the time decay estimates L-1(R) -> L infinity(R) is in vertical bar t vertical bar(-1/2) with a constant independent of the circumference of the circle. Our proof is based on an appropriate…

Journal of Mathematical Analysis and Applications, 2017, 448 (1), pp.262-280. ⟨10.1016/j.jmaa.2016.10.060⟩. ⟨hal-02152586⟩

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⟩

Chapitre d'ouvrage

Sintering of Ceramics

Anne Leriche, Stuart Hampshire, Francis Cambier

This chapter gives an overview of surface and bulk matter transport processes occurring during the densification of ceramic powder compacts. Starting from purified or chemically synthesized raw materials, sintering takes place by either solid state or liquid phase mechanisms during heat treatment…

Reference Module in Materials Science and Materials Engineering, Elsevier, 2017, ⟨10.1016/B978-0-12-803581-8.10288-7⟩. ⟨hal-03066533⟩

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

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

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⟩