Search results for "DIR"

On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

2016

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Hölder stability for Serrin’s overdetermined problem

2015

In a bounded domain \(\varOmega \), we consider a positive solution of the problem \(\Delta u+f(u)=0\) in \(\varOmega \), \(u=0\) on \(\partial \varOmega \), where \(f:\mathbb {R}\rightarrow \mathbb {R}\) is a locally Lipschitz continuous function. Under sufficient conditions on \(\varOmega \) (for instance, if \(\varOmega \) is convex), we show that \(\partial \varOmega \) is contained in a spherical annulus of radii \(r_i 0\) and \(\tau \in (0,1]\). Here, \([u_\nu ]_{\partial \varOmega }\) is the Lipschitz seminorm on \(\partial \varOmega \) of the normal derivative of u. This result improves to Holder stability the logarithmic estimate obtained in Aftalion et al. (Adv Differ Equ 4:907–93…

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996

ANALYSIS OF A SPHERICAL HARMONICS EXPANSION MODEL OF PLASMA PHYSICS

2004

A spherical harmonics expansion model arising in plasma and semiconductor physics is analyzed. The model describes the distribution of particles in the position-energy space subject to a (given) electric potential and consists of a parabolic degenerate equation. The existence and uniqueness of global-in-time solutions is shown by semigroup theory if the particles are moving in a one-dimensional interval with Dirichlet boundary conditions. The degeneracy allows to show that there is no transport of particles across the boundary corresponding to zero energy. Furthermore, under certain conditions on the potential, it is proved that the solution converges in the long-time limit exponentially f…

Nonlocal elasticity and related variational principles

2001

Abstract The Eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied. The model is refined by assuming an attenuation function depending on the `geodetical distance' between material particles, such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented. A suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model. The nonlocal elasticity boundary-value problem for infinitesimal displacements and quasi-static loads is addressed and the conditions for the solution uniqueness are established. Three variational principles, nonlocal…

The Nitsche phenomenon for weighted Dirichlet energy

2018

Abstract The present paper arose from recent studies of energy-minimal deformations of planar domains. We are concerned with the Dirichlet energy. In general the minimal mappings need not be homeomorphisms. In fact, a part of the domain near its boundary may collapse into the boundary of the target domain. In mathematical models of nonlinear elasticity this is interpreted as interpenetration of matter. We call such occurrence the Nitsche phenomenon, after Nitsche’s remarkable conjecture (now a theorem) about existence of harmonic homeomorphisms between annuli. Indeed the round annuli proved to be perfect choices to grasp the nuances of the problem. Several papers are devoted to a study of d…

A new force field including charge directionality for TMAO in aqueous solution

2016

We propose a new force field for trimethylamine N-oxide (TMAO), which is designed to reproduce the long-lived and highly directional hydrogen bond between the TMAO oxygen (OTMAO) atom and surrounding water molecules. Based on the data obtained by ab initio molecular dynamics simulations, we introduce three dummy sites around OTMAO to mimic the OTMAO lone pairs and we migrate the negative charge on the OTMAO to the dummy sites. The force field model developed here improves both structural and dynamical properties of aqueous TMAO solutions. Moreover, it reproduces the experimentally observed dependence of viscosity upon increasing TMAO concentration quantitatively. The simple procedure of the…

Modes of motion in a confined colloidal suspension under shear

2004

We investigated aqueous suspensions of charged polystyrene latex spheres at low salt concentration under the combined influence of steady shear and confining walls. Their equilibrium structure was adjusted via the particle and salt concentration to be either fluid or body centred cubic. Using high-resolution real-space microscopy, we here present a first direct observation of collective modes of motion under shear. As a function of either shear rate and/or salt concentration, we find a continuous transition from registered to free sliding of layers accompanied by an equally continuous structural rearrangement lowering the dimensionality of long-ranged order.

L'assureur peut-il opposer à la victime, qui exerce l'action directe contre l'assureur de l'auteur du dommage, la clause compromissoire contenue dans…

2022

(Versailles 21 janv. 2021, no 19/02675, SAS Rohlig France c/ Sté Vincy Construction Grands Projet, Rev. arb. 2021. 844, note J. Billemont)

La soumission de l'arbitrage international à un régime protecteur du consommateur

2021

International audience; (Civ. 1re, 30 septembre 2020, n° 18-19.241, D. 2020. 2501, note D. Mouralis ; ibid. 2484, obs. T. Clay ; AJ contrat 2020. 485, obs. D. Mainguy ; RTD civ. 2020. 845, obs. L. Usunier ; Dalloz actualités, 19 octobre 2020, 1949, obs. J. Jourdan-Marques ; JCP 2020, 311, note M. de Fontmichel ; JDI 2020. 1307, note E. Gaillard)