Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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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 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 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).Item THE SCHAUDER BASIS IN SYMMETRICALLY NORMED IDEALSOF OPERATORS(Institutul de Matematică şi Informatică al AŞM, 2004) Spinu, EfimiiIn this paper we build a basis in a separable symmetrically normed ideal.Item ABSOLUTE ASYMPTOTIC STABILITY OF DISCRETE LINEAR INCLUSIONS(Institutul de Matematică şi Informatică al AŞM, 2006) Cheban, David; Mammana, CristianaThe article is devoted to the study of absolute asymptotic stability of discrete linear inclusions in Banach (both finite and infinite dimensional) space. We establish the relation between absolute asymptotic stability, asymptotic stability, uniform asymptotic stability and uniform exponential stability. It is proved that for asymptotical compact (a sum of compact operator and contraction) discrete linear inclusions the notions of asymptotic stability and uniform exponential stability are equivalent. It is proved that finite-dimensional discrete linear inclusion, defined by matrices {A1,A2, ...,Am}, is absolutely asymptotically stable if it does not admit nontrivial bounded full trajectories and at least one of the matrices {A1,A2, ...,Am} is asymptotically stable. We study this problem in the framework of non-autonomous dynamical systems (cocyles).Item COLLOCATION AND QUADRATURE METHODS FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS(Institutul de Matematică şi Informatică al AŞM, 2006) Capcelea, TituThe computation schemes of collocation and mechanical quadraturemethods for approximate solving of the complete singular integral equations withpiecewise continuous coefficients and a regular kernel with weak singularity are elab-orated. The case when the equations are defined on the unit circumference of thecomplex plane is examined. The sufficient conditions for the convergence of thesemethods in the spaceL2are obtained.Item ON THE DIVISION OF ABSTRACT MANIFOLDS IN CUBES(Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Mariana; Cataranciuc, Sergiu; Soltan, PetruWe prove that in the class of abstract multidimensional manifolds withoutborders only torusVn1of dimensionn≥1 can be divided in abstract cubes with theproperty: every faceImfromVn1is shared by 2n−mcubes,m= 0,1, . . . , n−1. Theabstract torusVn1is realized inEd, n+1≤d≤2n+1, so it results that in the class ofalln-dimensional combinatorial manifolds [1]onlytorus respects this propriety. Torusis autodual because of this propriety.Item NUMERICAL TREATMENT OF THE KENDALL EQUATIONIN THE ANALYSIS OF PRIORITY QUEUEING SYSTEMS(Institutul de Matematică şi Informatică al AŞM, 2006) Bejan, AndreiWe investigate here how to treat numerically the Kendall functional equa-tion occuring in the theory of branching processes and queueing theory. We discussthis question in the context of priority queueing systems with switchover times. Innumerical analysis of such systems one deals with functional equations of the Kendalltype and efficient numerical treatment of these is necessary in order to estimate im-portant system performance characteristics.