Главная

Sergey A. Denisov

  1. Multidimensional L2 conjecture: a survey.

    Ср, 03/21/2012 - 15:01 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    In this survey, we give a short overview of the recent progress on the
    multidimensional L2 conjecture. It can also serve as an introduction to the
    subject.

  2. The sharp corner formation in 2d Euler dynamics of patches: infinite double exponential rate of merging.

    Чт, 01/12/2012 - 15:01 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    For the 2d Euler dynamics of patches, we investigate the convergence to the
    singular stationary solutions in the presence of a regular strain. The rate of
    merging as well as the growth of curvature are shown to be double exponential.

  3. An evolution equation as the WKB correction in long-time asymptotics of Schrodinger dynamics.

    Втр, 09/01/2009 - 12:47 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    We consider 3d Schrodinger operator with long-range potential that has
    short-range radial derivative. The long-time asymptotics of non-stationary
    problem is studied and existence of modified wave operators is proved. It turns
    out, the standard WKB correction should be replaced by the solution to certain
    evolution equation.

  4. Continuous analogs of polynomials orthogonal on the unit circle. Krein systems.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Classical Analysis and ODEs
    Abstract

    This survey contains the introduction to the subject. Many new results are
    also included.

  5. On a conjecture by Y. Last.

    Чт, 08/27/2009 - 13:23 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Classical Analysis and ODEs
    Abstract

    We prove a conjecture due to Y. Last on Jacobi matrices.

  6. Schrodinger operators and associated hyperbolic pencils.

    Чт, 08/27/2009 - 13:23 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Spectral Theory
    Abstract

    For a large class of Schrodinger operators, we introduce the hyperbolic
    quadratic pencils by making the coupling constant dependent on the energy in
    the very special way. For these pencils, many problems of scattering theory are
    easier to study. Then, we give some applications to the original Schrodinger
    operators.

  7. Infinite superlinear growth of the gradient for the two-dimensional Euler equation.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    For two-dimensional Euler equation on the torus, we prove that the uniform
    norm of the gradient can grow superlinearly for some infinitely smooth initial
    data. We also show the exponential growth of the gradient for the finite time.

  8. Wave equation with slowly decaying potential: asymptotics and wave operators.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    For the one-dimensional case, we establish the long-time asymptotics of
    solution to Cauchy problem and prove existence of modified wave operators. In
    particular, we show that the part of the wave travels ballistically if the
    potential is square summable and this result is sharp.

  9. Weak asymptotics for Schrodinger evolution.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    We apply technique developed in [2] to study the long-time behavior of
    Schrodinger evolution.

  10. The generic behavior of solutions to some evolution equations: asymptotics and Sobolev norms.

    Втр, 08/18/2009 - 11:53 — SomNambul
    Authors: Sergey A. Denisov
    Subjects: Analysis of PDEs
    Abstract

    We study generic behavior of solutions to a large class of evolution
    equations. The methods are applied to Schrodinger evolution on the circle.

Math-arch

RSS-материал