In this paper we have placed a particular emphasis on the construction of the algorithmic scheme leading to the codes to identify the parameters of the silting of the banks of the rivers. To overcome the lack of real field data, we generated experimental data by solving a carefully chosen partial differential equation . All the codes obtained were executed on the Matlab 7.14(R2012 a) interface and the results of the simulation were satisfactory.

Abstract In this paper, we are interested in the computation of the unknown initial state for the simulation and prediction of PDE systems where the solution measures are partially known over a time interval. Such a problem is usually solved by an ill-posed optimal control problem. Based on an appropriate collocation approximation, we obtain a discrete inverse problem. To solve this problem, a non-standard discrete approach is used. This allows to obtain a transformation of the original problem into a well-posed ones based on the zero controllability of a discrete system. The desired control is then calculated as well as the discrete approximation of the initial state values. Mathematics Subject Classification. 35K55; 35J60; 80A22.

The river silting process is complex and represents one of the greatest challenges faced in the future. In this paper, we propose an asymptotic approach for describing silting of rivers to study asymptotic solutions governing a coupled (hydro-sedimentary) model. We focus our paper on the inner and outer asymptotic expansions of solutions. The proposed approach is based on the hypothesis that rivers silting can be explain by an asymptotic behavior near shock curves of the governing equations of sediment deposits. We look for an inner and outer asymptotic expansion which gives us expressions of the solution in the neighborhood of the shock zone. Once both asymptotic expansions found , we give matching property of both expansions. Mathematics Subject Classification: 65M70; 65N22 162 Y. A. S. Wellot et al.

The phenomenon of extinction is an important property of solutions for many evolutionary equa-tions. In this paper, a numerical simulation for computing the extinction time of nonnegative solu-tions for some nonlinear parabolic equations on general domains is presented. The solution algo-rithm utilizes the Donor-cell scheme in space and Euler’s method in time. Finally, we will give some numerical experiments to illustrate our algorithm.

This paper proposes an approach for determining solutions sets of larger scale non linear equations systems with more unknowns number than equations.The proposed approach consists in transforming the equations system into a one dimensional equation by using α-dense curves properties.Then conditions for obtaining sets that are dense in the set of solution is established.An example is provided to demonstrate merits of our proposed algorithm.

The study of the influence of sediments brought on the sedimentary bottom formation and evolution of rivers or lakes presents a big scientific interest both by its interdisciplinary aspect and by its importance.In this work, we propose to associate the hydrodynamic and geological points with a view to establish a continuous model of the sedimentary bottom evolution processes based on conservation mass law.This model, general and progressive, make it possible to consider the flocculation phenomenon, geological activities of the bottom, and other.We establish later on the conditions of existence of admissible solutions where sedimentation is more important than the erosion process.

In this work, we give a general overview on pseudo-spectral meth- ods. Three types of its variants which are: the adaptive spectral methods conceived for functions with rapid variation in certain domains, the rational adaptive spectral method using rational interpolants, and the adaptive grid Chebyshev points thanks to conformal maps, another type of approximation by the Chebyshev spectral method constituted by a collection of algorithms coded in an objet-oriented MATLAB software environment are considered.

This paper deals with the analysis of the local and global stability of an modified age-structured model for the transmission dynamics of hepatitis B without vertical transmission. The proposed model takes into account the additional mortality rate associated to the desease and incorporates vaccination strategy.

Free space optical systems are potential candidates of large band spatial transmission solutions. This article investigates on the impact of relays to mitigate the zenith angle in the performance of a Free Space Optical (FSO) transmission. The high earth orbit communication channel has been approximated by considering the complexity of the atmosphere in two layers. The influence of zenith angle on the quality of the link has been evaluated. Appropriate network architecture scheme has been proposed. It is shown that it is possible to get a BER of 10-5 even when a zenith angle of 76.1° is considered.

We present a practical technique for calculating adjoint codes arising in variational methods for data assimilation. Our aim is to bring a more to the automatic differentiation in the MatLab langage. It is used to identify the initial condition of the problem governed by a non linear partial differential equation. The cost function gradient’s is derived by using the discrete adjoint model. Numerical examples are presented for Kardar-Parisi-Zhang equation using explicit Euler discretisation in time and pseudo-spectral discretisation in the 2D space dimension. The numerical results obtained from the MatLab environment allow us to verify the efficient of this scheme.

This paper aims at using of an approach integrating the fuzzy logic strategy for hypoxemic hypoxia tissue blood carbon dioxide human optimal control problem. To test the efficiency of this strategy, the authors propose a numerical comparison with the direct method by taking the values of determinant parameters of cardiovascular-respiratory system for a 30 years old woman in jogging as her regular physical activity. The results are in good agreement with experimental data.