Oberseminar Dynamische Systeme und Kontrolltheorie

Vorträge

  • Montag, 17.10.2016, 11:00 Uhr, Raum 01.003, Mathematikgebäude Ost

    Prof. Dr. Oleksiy Kapustyan, Taras Shevchenko National University of Kyiv, Ukraine

    Title:
    GLOBAL ATTRACTORS THEORY AND ITS APPLICATION TO EVOLUTIONARY SYSTEMS WITHOUT UNIQUENESS AND IMPULSIVE SYSTEMS

    Abstract:

    The report focuses on the study of the qualitative behavior of solutions of evolution equations by the methods of the theory of global attractors. The main emphasis is on the dissipative systems, the initial state of which do not uniquely determine their future behavior. Using well-known infinite-dimensional systems (reaction-diffusion systems, 3D Navier-Stokes systems) we analyze in detail the basic concepts, notions, results, their possible applications and open problems. Also we give an application of global attractors theory to impulsive infinite-dimensional dynamical systems.

  • Donnerstag, 27.11.2016, 11:00 Uhr, Raum 01.003, Mathematikgebäude Ost

    Prof. Dr. Snezhana Hristova, Plovdiv University, Bulgaria

    Title:
    DIFFERENTIAL EQUATIONS WITH "MAXIMA"

    Abstract:

    Differential equations with "maxima" are a special type of differential equations that contain the maximum of the unknown function over a previous interval(s). Such equations adequately model real world processes whose present state significantly depends on the maximum value of the state on a past time interval. For example, in the theory of automatic control in various technical systems often the law of regulation depends on the maximum values of some regulated state parameters over certain time intervals. This requires the use of differential equations with ``maxima'' in the control theory. Recently, the interest in differential equations with "maxima" has increased. The theoretical investigations of differential equations with "maxima" opens the door to enormous possibilities for modeling of real world processes and phenomena. In the present talk a gentle introduction to the theory of differential equations with "maxima" will be given. Some qualitative properties of the solutions will be given. An approximate method for their solving will be introduced. Some new open problems will be set up.

  • Freitag, 4.11.2016

    Anastasiia Karas, Uni Würzburg

    Title:
    Inlet and outlet boundary conditions for high Reynolds incompressible flows

    Abstract:

    A common way to compute the flow around an object (such as the classical case of a flux around the obstacle, for instance) is to truncate the physical domain so as to obtain a suitable computational domain. Therefore, an artificial boundary conditions on the non-physical part of the boundary should be prescribed. In the talk I will present my Master's Diplome Project, written under the guidance of Prof. C.Galusinski (Toulon University, France) about inlet and outlet boundary conditions for high Reynolds incompressible flows in open domains. Such a type of boundary conditions is called “traction“ boundary conditions and they were first introduced by C.-H. Bruneau (2000). By analysis of the resulting system we prove the control of the energy of the system with the use of "traction" boundary conditions and also we implement them in code "BiNSi" solving Navier-Stokes equations on general geometry.

  • Freitag, 10.2.2017

    Dr. Andrii Mironchenko, Uni Passau

    Title and abstract: tba

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