Convergence of optimal control problems governed by second kind parabolic variational inequalities

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal controls and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011

Unsteady 3D-Navier-Stokes System with Tresca's Friction Law

Motivated by extrusion problems, we consider a non-stationary incompress-ible 3D fluid flow with a non-constant (temperature dependent) viscosity, subjected to mixed boundary conditions with a given time dependent velocity on a part of the boundary and Tresca's friction law on the other part. We construct a sequence of approximate solutions by using a regularization of the free boundary condition due to friction combined with a particular penalty method, reminiscent of the " incompressibility limit " of compressible fluids, allowing to get better insights into the links between the fluid velocity and pressure fields. Then we pass to the limit with compactness arguments to obtain a solution to our original problem

Existence result for a strongly coupled problem with heat convection term and Tresca's law.

International audienceWe study a problem describing the motion of an incompressible, nonisothermal and non-Newtonian uid, taking into account the heat convection term. The novelty here is that uid viscosity depends on the temperature, the velocity of the uid, and also of the deformation tensor, but not explicitly. The boundary conditions take into account the slip phenomenon on a part of the boundary of the domain. By using the notion of pseudo-monotone operators and xed point Theorem we prove an existence result of its weak solution

The Neumann problem in thin domains with very highly oscillatory boundaries

In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\epsilon = \{(x_1,x_2) \in \R^2 \; | \; x_1 \in (0,1), \, - \, \epsilon \, b(x_1) < x_2 < \epsilon \, G(x_1, x_1/\epsilon^\alpha) \}$ with $\alpha>1$ and $\epsilon > 0$, defined by smooth functions $b(x)$ and $G(x,y)$, where the function $G$ is supposed to be $l(x)$-periodic in the second variable $y$. The condition $\alpha > 1$ implies that the upper boundary of this thin domain presents a very high oscillatory behavior. Indeed, we have that the order of its oscillations is larger than the order of the amplitude and height of $R^\epsilon$ given by the small parameter $\epsilon$. We also consider more general and complicated geometries for thin domains which are not given as the graph of certain smooth functions, but rather more comb-like domains.Comment: 20 pages, 4 figure

TDAE Strategy in the Benzoxazolone Series: Synthesis and Reactivity of a New Benzoxazolinonic Anion

International audienceWe describe an original pathway to produce new 5-substituted 3-methyl-6-nitro-benzoxazolones by the reaction of aromatic carbonyl and α-carbonyl ester derivatives with a benzoxazolinonic anion formed exclusively via the TDAE strategy

A Heat Conduction Problem with Sources Depending on the Average of the Heat Flux on the Boundary

Motivated by the modeling of temperature regulation in some mediums, we consider the non-classical heat conduction equation in the domain D=\mathbb{R}^{n-1}\times\br^{+} for which the internal energy supply depends on an average in the time variable of the heat flux $(y, s)\mapsto V(y,s)= u_{x}(0 , y , s)$ on the boundary $S=\partial D$. The solution to the problem is found for an integral representation depending on the heat flux on $S$ which is an additional unknown of the considered problem. We obtain that the heat flux $V$ must satisfy a Volterra integral equation of second kind in the time variable $t$ with a parameter in $\mathbb{R}^{n-1}$. Under some conditions on data, we show that a unique local solution exists, which can be extended globally in time. Finally in the one-dimensional case, we obtain the explicit solution by using the Laplace transform and the Adomian decomposition method.Comment: Accepted by Revista UMA, April 30 2019, in press. arXiv admin note: substantial text overlap with arXiv:1610.0168

A Robust Approach to Characterize the Human Ear: Application to Biometric Identification

The Human ear is a new technology of biometrics which is not yet used in a real context or in commercial applications. For this purpose of biometric system, we present an improvement for ear recognition methods that use Elliptical Local Binary Pattern operator as a robust descriptor for characterizing the fine details of the two dimensional ear imaging. The improvements are focused on features extractions and dimensionalities reductions steps. The realized system is mainly appropriate for identification mode; it starts by decomposing the normalized ear image into several blocks with different resolutions. Next, the local textural descriptor is applied on each decomposed block. A problem of information redundancies is appeared due to the important size of the concatenated histograms of all blocks, which has been resolved by reducing of the histogram’s dimensionalities and by selecting the pertinent information using Haar Wavelets. Finally, the system is evaluated on the IIT Delhi Database containing two dimensional ear images and we have obtained a success rate about 97% for 493 images from 125 persons and about 96% for 793 images from 221 persons