2. Articole
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Item LIMITS OF SOLUTIONS TO THE SEMILINEAR WAVE EQUATION WITH SMALL PARAMETER(Academia de Ştiinţe a Moldovei, 2006) Perjan, AndreiWe study the existence of the limits of solution to singularly perturbed initial boundary value problem of hyperbolic - parabolic type with boundary Dirichlet condition for the semilinear wave equation. We prove the convergence of solutions and also the convergence of gradients of solutions to perturbed problem to the corresponding solutions to the unperturbed problem as the small parameter tends to zero. We show that the derivatives of solution relative to time-variable possess the boundary layer function of the exponential type in the neighborhood of t = 0Item LINEAR SINGULAR PERTURBATIONS OF HYPERBOLIC-PARABOLIC TYPE(Academia de Ştiinţe a Moldovei, 2003) Perjan, AndreiWe study the behavior of solutions of the problem εu′′(t)+u′(t)+Au(t) =f (t), u(0) = u0, u′(0) = u1 in the Hilbert space H as ε → 0, where A is a linear,symmetric, strong positive operator.Item INVARIANT MANIFOLDS, GLOBAL ATTRACTORS AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS DIFFERENCE EQUATIONS(Elsevier, 2004) Cheban, David; Mammana, CristianaThe article is devoted to the study of quasi-linear nonautonomous difference equations: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets. First, we prove that such equations admit an invariant continuous section (an invariant manifold). Then, we obtain the conditions for the existence of a compact global attractor and characterize its structure. Third, we derive a criterion for the existence of almost periodic and recurrent solutions of the quasi-linear nonautonomous difference equations. Finally, we prove that quasi-linear maps with chaotic base admit a chaotic compact invariant set. The obtained results are applied while studying triangular maps: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets.Item ALMOST PERIODIC SOLUTIONS AND GLOBAL ATTRACTORS OF NON-AUTONOMOUS NAVIER–STOKES EQUATIONS(Springer, 2004) Cheban, David; Duan, JinqiaoThe article is devoted to the study of non-autonomous Navier–Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier–Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic, almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier–Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier–Stokes equations.Item ERGODIC SETS AND MIXING EXTENSIONS OF TOPOLOGICAL TRANSFORMATION SEMIGROUPS(Institutul de Matematică şi Informatică al AŞM, 2003) Gerco, AnatolieWe extend the concept of the ergodic set [1] – [2] from topological trans-formation groups to topological transformation semigroups. We investigate, in par-ticular, connections between ergodicity, weak ergodicity, topological transitivity andminimality of the Whitney’s sum of extensions of topological transformation semi-groupsItem SINGULAR PERTURBATIONS OFHYPERBOLIC-PARABOLIC TYPE(Institutul de Matematică şi Informatică al AŞM, 2003) Perjan, AndreiWe study the behavior of solutions of the problemεu′′(t)+u′(t)+Au(t) =f(t), u(0) =u0, u′(0) =u1in the Hilbert spaceHasε→0, whereAis a linear,symmetric, strong positive operator.Item ON STRONG STABILITY OF LINEAR POISSON ACTIONS(Institutul de Matematică şi Informatică al AŞM, 2003) Glavan, Vasile; Rzeszotko, Z.Linear Poisson actions of the groupRmare considered. Conditions on thejoint spectrum of the generators and on the centralizers assuring stability and strongstability of the action are given. We give also some examplesof Poisson actions usingCAS”Mathematica”.Item GLOBAL ATTRACTORS FOR V -MONOTONE NONAUTONOMOUS DYNAMICAL SYSTEMS(Institutul de Matematică şi Informatică al AŞM, 2003) Cheban, David; Kloeden, Peter-E.; Schmalfuss, BjornThis article is devoted to the study of the compact global atrractors of Vmomotone nonautonomous dynamical systems.We give a description of the structure of compact global attractors of this class of systems. Several applications of general results for different classes of differential equations (ODEs, ODEs with impulse, some classes of evolutionary partial differential equations) are given.Item THE OPTIMAL FLOW IN DYNAMIC NETWORKSWITH NONLINEAR COST FUNCTIONS ON EDGES(Institutul de Matematică şi Informatică al AŞM, 2004) Fonoberova, Maria; Lozovanu, DmitriiIn this paper we study the dynamic version of the nonlinear minimum- cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is based on reducing the dynamic problem to the classical minimum-cost problem on a time-expanded network. We also study some generalization of the proposed problem.Item ASYMPTOTIC STABILITY OF AUTONOMOUSAND NON-AUTONOMOUS DISCRETE LINEAR INCLUSIONS(Institutul de Matematică şi Informatică al AŞM, 2004) Cheban, David; Mammana, CristianaThe article is devoted to the study of absolute asymptotic stability ofdiscrete linear inclusions (both autonomous and non-autonomous) in Banach space.We establish the relation between absolute asymptotic stability, uniform asymptoticstability and uniform exponential stability. It is proved that for compact (completelycontinuous) discrete linear inclusions these notions of stability are equivalent. Westudy this problem in the framework of non-autonomous dynamical systems (cocyles).