Said Mesloub

On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

On the application of the homotopy analysis method for a nonlocal mixed problem with Bessel operator

Abstract In this research work, we give analytic approximate solutions for a nonlocal initial boundary value problem where one of the classical conditions is replaced by an integral condition by employing the homotopy analysis method (HAM). The series solution can be obtained by either using initial conditions (partial t -solution) or by using the boundary conditions (partial x -solution). This method allows us to control the convergence region of the series solution.

On an evolution-mixed thermoelastic system problem

This paper deals with the study of an initial boundary value problem for a thermoelastic system. We first give some existence and uniqueness results of the solution and then numerical solutions for the system are derived by using finite-difference methods. Iterative schemes with second-order accuracy are derived. An illustrative numerical example with a graphical representation illustrates the efficiency of the derived numerical schemes.

Application of double Laplace decomposition method to solve a singular one-dimensional pseudohyperbolic equation

In this work, the double Laplace decomposition method is applied to solve singular linear and nonlinear one-dimensional pseudohyperbolic equations. This method is based on double Laplace transform and decomposition methods. In addition, we prove the convergence of our method. This method is described and illustrated by some examples. These results show that the introduced method is highly accurate and easy to apply.

On the numerical solution of a singular second-order thermoelastic system

In this article, we study an initial boundary value problem for a coupled system of thermoelasticity. Some existence and uniqueness results are given. The homotopy analysis method is employed to obtain numerical schemes for solving the posed problem. The efficiency of the derived methods is illustrated through several examples with graphical representations.

A numerical solution of two-dimensional fox-rabies dynamics of advection type

This article analyses a mode of two-dimensional fox-rabies dynamics with advection terms. The fox population is divided into two species: susceptible S and infective I. Finite-difference techniques are employed to compute the numerical solutions of this model. Iterative schemes with second-order accuracy are derived and their convergence is investigated by using the maximum principle analysis. An illustrative numerical example with graphical reis given to highlight the efficiency of the derived numerical schemes.

On a coupled fourth order thermoelastic system with nonlocal constraints

In this paper, we establish the existence and uniqueness of the strong generalized solution of an initial boundary value problem for a coupled fourth order thermoelastic system with nonlocal constraints, which arise mainly in linear thermoelasticity. The system modelizes a Kirchof plate. Some energy and a priori estimates and density arguments are used in our proofs.