Blar i forfatter "Piatnitski, Andrei"

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    • Homogenization of Ferromagnetic Energies on Poisson Random Sets in the Plane 

      Braides, Andrea; Piatnitski, Andrei (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-01-06)
      We prove that by scaling nearest-neighbour ferromagnetic energies de ned on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on proving that cells with `very long' or `very short' edges of the corresponding Voronoi tessellation can be neglected. In this way we may apply Geometry Measure ...

    • Homogenization of Non-Autonomous Operators of Convolution Type in Periodic Media<sup>∗</sup> 

      Piatnitski, Andrei; Zhizhina, Elena (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-23)
      The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scaling is diffusive that is the scaling factor of the temporal variable is equal to the square of ...

    • Homogenization of the linearized ionic transport equations in random porous media 

      Mikelić, Andro; Piatnitski, Andrei (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-06-13)
      In this paper we obtain the homogenization results for a system of partial differential equations describing the transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid random disperse porous medium. We present a study of the nonlinear Poisson–Boltzmann equation in a random medium, establish convergence of the stochastic homogenization procedure and prove well-posedness ...

    • Large deviations for Markov jump processes in periodic and locally periodic environments 

      Piatnitski, Andrei; Pirogov, Sergei; Zhizhina, Elena (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-12)
      The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating locally periodic coefficient and, under natural ellipticity and localization conditions, show that the family satisfies the large deviation principle in the path space ...

    • On operator estimates in homogenization of nonlocal operators of convolution type 

      Piatnitski, Andrei; Sloushch, Vladimir; Suslina, Tatiana; Zhizhina, Elena (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-01-11)

    • On the spectrum of convolution operator with a potential 

      Borisov, D.I.; Piatnitski, Andrei; Zhizhina, E.A. (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-08-09)
      This paper focuses on the spectral properties of a bounded self-adjoint operator in <b><i>L</i><sub>2</sub></i></b>(R<sup>d</sup>) being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential converging to zero at infinity. We study both the essential and the discrete spectra of this operator. It is shown that the essential ...

    • Spectrum of One-Dimensional Potential Perturbed by a Small Convolution Operator: General Structure 

      Borisov, D.I.; Piatnitski, Andrei; Zhizhina, E.A. (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-09-23)
      We consider an operator of multiplication by a complex-valued potential in L<sub>2</sub>(R), to which we add a convolution operator multiplied by a small parameter. The convolution kernel is supposed to be an element of L<sub>1</sub>(R), while the potential is a Fourier image of some function from the same space. The considered operator is not supposed to be self-adjoint. We find the essential spectrum ...