Related papers: Homogeneous linear matrix difference equations of …
The main objective of this talk is to develop a matrix pencil approach for the study of an initial value problem of a class of singular linear matrix differential equations whose coefficients are constant matrices. By using matrix pencil…
In this article, we study a boundary value problem of a class of singular linear discrete time systems whose coefficients are non-square constant matrices or square with a matrix pencil which has an identically zero determinant. By taking…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
In this article we focus our attention on the relation between a singular linear discrete time system and a singular linear system of fractional nabla difference equations whose coefficients are square constant matrices. By using matrix…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
We study the analytic properties of a matrix discrete system introduced in [7]. The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix…
In this article we study the causality of non-homogeneous linear singular discrete time systems whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space sampling instants we provide…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model…
In this paper we establish existence, nonexitence and regularity of positive solutions for a class of singular quasilinear elliptic systems subject to (super-) homogeneous condition. The approach is based on sub-supersolution methods for…
This paper concerns a space-time homogenization limit of nonnegative weak solutions to porous medium equations. In particular, the so-called homogenized matrix will be characterized in terms of solutions to cell problems, which drastically…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
The problem of determining whether a diagonally dominant matrix is singular or nonsingular is a classical topic in matrix theory. This paper develops necessary and sufficient conditions for the singularity or nonsingularity of diagonally…
In this short paper we identify special systems of (an arbitrary number) N of first-order Difference Equations with nonlinear homogeneous polynomials of arbitrary degree M in their right-hand sides, which feature very simple explicit…
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…