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In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term. [ABSTRACT FROM AUTHOR]

This study aims to investigate numerically and theoretically a thermoelastic Bresse system where the heat conduction given by the Green and Naghdi theories. Theoretically, we establish the existence and uniqueness of solutions as well as the exponential stability regardless of the system's parameters. Numerically, we present a finite element approximation, and we show the discrete energy decay. At the end, we provide some numerical results with an error estimate based on additional regularity of the solution. [ABSTRACT FROM AUTHOR]

The paper deals with the study of the existence result for a Kirchhoff elliptic system with additive right-hand side and variable parameters by using the sub-/supersolution method. Our study is a natural extension result of our previous one in (Boulaaras and Guefaifia in Math. Methods Appl. Sci. 41:5203–5210, 2018), where we discussed only the simple case when the parameters are constant. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of parabolic variational inequalities with nonlinear source terms, where the existence and uniqueness of the solution is provided by using Banach's fixed point theorem. In addition, an optimally L ∞ -asymptotic behavior is proved using Euler time scheme combined with the finite element spatial approximation. The approach is based on Bensoussan–Lions algorithm for evolutionary free boundary problems using the concepts of subsolutions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton-Jacobi-Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L -convergence of a piecewise linear finite element method is established using the concept of subsolution. [ABSTRACT FROM AUTHOR]

In this article, an optimal error estimate for parabolic variational inequalities is studied. Existence and uniqueness of the solution is provided by the introduction of a constructive algorithm. An optimallyL∞-asymptotic behavior in uniform norm is proved using the semi-implicit time scheme combined with the finite element spatial approximation. The approach is based on the concept of subsolutions. [ABSTRACT FROM PUBLISHER]

In this paper, a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the interfaces, for parabolic variational equation with second order boundary value problems, are derived using the semi-implicit-time scheme combined with a finite element spatial approximation. Furthermore a result of asymptotic behavior in uniform norm is given using Benssoussan-Lions' algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the interfaces, for parabolic variational equation with second order boundary value problems, are derived using the semi-implicit-time scheme combined with a finite element spatial approximation. Furthermore a result of asymptotic behavior in uniform norm is given using Benssoussan-Lions' algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with a system of parabolic quasi-variational inequalities related to the management of energy production with mixed boundary condition. A quasi-optimal L-error estimate is established using a new discrete algorithm based on a theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L-stability property with respect to the right-hand side. [ABSTRACT FROM AUTHOR]

This paper is an extension and generalization of the previous results, cf. [2-4]. It is devoted to the theta-scheme with respect to the t -variable combined with a finite-element spatial approximation of the evolutionary Hamilton-Jacobi-Bellman equations (HJB equation) and involves a weakly coupled discrete system of parabolic quasi-variational inequalities (PQVs). Its relation to time energy behavior is proved. In addition, the PQVs are transformed into a coercive discrete system of elliptic quasi-variational inequalities. A new iterative discrete algorithm is also proposed to show the existence and uniqueness of the discrete solution. Moreover, its convergence is established. Then a simple proof to an asymptotic behavior in uniform norm is given. Furthermore the proposed approach is based on a discrete L-stability property with respect to the right-hand side and the boundary conditions. [ABSTRACT FROM AUTHOR]

Abstract: This paper is an extension for our previous results [3–5], and it deals with the finite element approximation of a parabolic quasi-variational inequalities with mixed boundary conditions. A quasi-optimal L ∞-error estimate is established using a new discrete algorithm stands in theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L ∞-stability property with respect to the right-hand side where the obstacle defined as an impulse control problem. [Copyright &y& Elsevier]

In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for quasi-variational inequalities related to impulse control problem with mixed boundary conditions. We provide that the discretization on every sub-domain converges in uniform norm. Furthermore, a result of approximation in uniform norm is given. [ABSTRACT FROM AUTHOR]

The paper deals with the theta time scheme combined with a finite element spatial approximation of parabolic variational inequalities. The parabolic variational inequalities are transformed into noncoercive elliptic variational inequalities. A simple result to time energy behavior is proved, and a new iterative discrete algorithm is proposed to show the existence and uniqueness. Moreover, its convergence is established. Furthermore, a simple proof to asymptotic behavior in uniform norm is given. [ABSTRACT FROM AUTHOR]

In the context of the development of the research project (Boulaaras et al.) which was supported by the Deanship of Scientific Research of Qassim University under the Project No. 1140 during the academic year 2016/1437, this research will introduce a two dimensional mathematical model based on the finite elements spatial method combined with a finite differences time scheme applied to the diffusion equations. This model will be applied in the hypothetical example where the obtained results will be compared with the real experimental data. Such a comparison will allow to predict the soil temperature for different depths and at different time periods according to certain conditions on the weather and take into account the stability conditions of the used numerical method. It's worthy of note that some of the concreted mathematical problems will be addressed by the experimental scientific theories of functional analysis and then the numerical simulation of the theoretical study will be provided thanks to sophisticated methods with more convergence and stability. This mathematical model would be reduced by means of physical measurement and also in charge of the physical cost. [ABSTRACT FROM AUTHOR]