This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations (DAEs). Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we...

Abstract We study the unique solvability of discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin finite element method. Well-posedness discrete equations is typically investigated by applying compact perturbation argument to continuous so that `sufficiently rich' discretization results in small' and well-posedness inherited via Fredholm’s alternative. The qua...

We prove a number of homeomorphism results for nonlinear Fredholm maps of index zero and their perturbations. Moreover, we show that k-ball and k-set perturbations of these homeomorphisms are again homeomorphisms or that the corresponding equations are finitely solvable. Various generalized first Fredholm theorems are given and finite solvability of general ( odd ) Fredholm maps is also studied...

The aim of this paper is to study the controllability of a system described by an integral inclusion of Urysohn type with delay. In our approach we reduce the controllability problem of the nonlinear system into solvability problem of another integral inclusion. The solvability of this integral inclusion is subsequently established by imposing suitable standard boundedness, convexity and semico...

We extend and analyse an enhanced approximate cloaking scheme, which was recently introduced by Ammari, Kang, Lee, and Lim [3] to cloak a domain with a fixed, homogeneous Neumann boundary condition. Subject to the solvability of a finite set of algebraic equations we construct an approximate cloak for the two dimensional transmission case, which achieves invisibility of the order ρ while mainta...

The cyclic scheduling problem modeled in terms of Cyclic Concurrent Process Systems is considered. The problem can be seen as a kind of Diophantine problem, hence its solvability, i.e. schedulability, plays a pivotal role in many supply-chain problems. In contradiction to the traditionally offered solutions the approach proposed allows one to take into account such behavioral features as transi...