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Workshop on Infinite-dimensional dynamical systems and attractors

日期:2020-08-15点击数:

August 17th-21st 2020, Lanzhou University, Lanzhou, China.

The aim of this Workshop is to bring together experts who works ondiverse frontiers of Infinite-dimensional dynamical systems andtheir applications to survey recent progress and current challenges.

VooV/Tencentmeeting webinar links:https://meeting.tencent.com/s/uiblXZG1vSTQMetting ID: 642 6164 2331

Topics:

  • Analysis of PDEs;

  • Dissipative Dynamics: Attractors; Inertialmanifolds;Random dynamics, etc.

  • Integral inequalities

    List of invited speakers:

    T.Dlotko (Silesian University, Poland)

    V.Kalantarov (Koch University, Turkey)

    P.Kloeden (Universität Tubingen, Germany)

    A.Kostianko (Lanzhou University, China)

    A.Ilin (Russian Academy of Sciences, Russia)

    A.Miranville (Université de Poitiers, France)

    D.Turaev (Imperial College London, UK)

    Short Classes:

    Sergey Zelik (Lanzhou University, China): Attractors intopological spaces and applications

    Organizing Committee:

    Anna Kostianko (Lanzhou University, a.kostianko@surrey.ac.uk)

    Shan Ma (Lanzhou University, mashan@lzu.edu.cn)

    Chunyou Sun (Lanzhou University, sunchy@lzu.edu.cn)

    Sergey Zelik (Lanzhou University, s.zelik@surrey.ac.uk)

    Chengkui Zhong (Nanjing University, ckzhong@nju.edu.cn)

    Program: see attachment.




  • Critical Parabolic Equations

    Tomasz Dlotko

    University of Silesia in Katowice, Poland

    We discuss the well-posedness and regularity for several parabolic-type equations. It basedon our recent monographCritical Parabolic-Type Problems, De Gruyter, 2020.


    Asymptotic regularity and attractors for slightly compressible

    Brinkman-Forchheimer equations

    Varga K. Kalantarov

    Ko¸c University, Istanbul; Azerbaijan State Oil and Industry University, Baku

    The talk will be devoted to the initial boundary value problems for slightly compressibleBrinkman-Forchheimer equations, modeling motion of flfluids in porous media. in a bounded 3Ddomain with suffiffifficiently smooth boundary under the homogeneous Dirichlet boundary condition.The dissipativity of the semigroup generated by the problem considered in higher order energyspaces is obtained, regularity and smoothing properties of solutions are studied. In addition, theexistence of a global and an exponential attractors for the semigroup generated by the problemin a natural phase space is verifified.


    Mean-square random dynamical systems and mean-square dichotomies

    Peter E. Kloeden

    Mathematisches Institut, Universita^¨t Tu^¨bingen, D-72076 Tu^¨bingen, Germany

    Mean-square random dynamical systems are essentially deterministic nonauton-omous dynamical systems defifined in terms of a two-paramater semigroup acting on a state space ofmean-square random variables. Many concepts of nonautonomous dynamical systems such aspullback attractors carry over, but there are practical diffiffifficulties in applying the known resultsdue to the lack of compactness criteria in such spaces. Such systems are generated by mean-fifield SDE, i.e., those involving expectations in their coeffiffifficients. The mean-square dichotomyspectrum and an example of bifurcation to a mean-square attractor will also be discussed.

    References

    [1] S.T. Doan, M. Rasmussen and P.E. Kloeden, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor,Discrete Conts. Dyn. Systems, Series B20, (2015), 875–887.

    [2] P.E. Kloeden and T. Lorenz, Mean-square random dynamical systems,J.Difffferential Equations253(2012), 1422–1438.1

    [3] P.E. Kloeden and T. Lorenz, Stochastic difffferential equations with nonlocal sample dependence,J.Stoch. Anal. Applns.,28(2010), 937-947.


    Lipschitz Mane projections and fifinite-dimensional reduction forcomplex Ginzburg-Landau equation

    Anna Kostianko

    Lanzhou University, China; Surrey University, UK

    In this talk I will discuss the problem of the fifinite-dimensional reduction for 3D complexGinzburg-Landau equation (GLE) with periodic boundary conditions. Using spatial averagingprinciple, which was introduced by J. Mallet-Paret and G. Sell to handle the 3D reactiondiffffusion equations, together with temporal averaging we will be able to show that the attractorof our problem possesses Man´e projections with Lipschitz continuous inverse. This work can beconsidered as the fifirst step to proof the existence of an inertial manifold for GLE.


    Lieb-Thirring and Ladyzhenskaya inequalities on the the 2dsphere and on the 2d torus

    Alexey A. Ilyin

    Russian Academy of Sciences, Russia

    We prove on the 2d sphere and on the 2d torus the Lieb–Thirring inequalities with improvedconstants for orthonormal families of scalar and vector functions. It is a joint work with A.Laptevand S.Zelik.


    Mathematical models for glial cells

    Alain Miranville

    Universit de Poitiers, France

    Our aim in this talk is to discuss mathematical models for glial cells and energy metabolismin the brain. In particular we discuss the existence of global in times solutions for a Cahn-Hilliardtype model.


    On triple instability

    Dmitry Turaev

    Imperial College London, UK

    It is well-known that bifurcations of a triply unstable equilibrium or a periodic orbit canlead to the emergence of chaotic dynamics. We show that the richness and complexity of thesedynamics are unrestricted.