9 papers
Convergence to global equilibrium for the semiconductor Boltzmann equation
Gayrat Toshpulatov
The Boltzmann equation describing the transport of electrons in semiconductor devices with an external electrostatic potential is considered when the spatial variable is in a torus…
Sharp estimates for the Fourier transform of surface-carried measures and maximal operators associated with hypersurfaces in with vanishing Gaussian curvature
Isroil A. Ikromov, Gayrat Toshpulatov
In this paper, we study problems related to harmonic analysis on hypersurfaces in with zero Gaussian curvature and given as graphs of polynomial functions. We deriv…
Long time behavior of Fokker-Planck equations for bosons and fermions
Anton Arnold, Marlies Pirner, Gayrat Toshpulatov
This paper is concerned with space inhomogeneous quantum Fokker-Planck equations posed on a classical kinetic phase space. The nonlinear factor appears both in the tran…
Long time behavior of discrete velocity kinetic equations
Gayrat Toshpulatov
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time d…
Hypocoercivity for the non-linear semiconductor Boltzmann equation
Marlies Pirner, Gayrat Toshpulatov
A kinetic model for semiconductor devices is considered on a flat torus. We prove exponential decay to equilibrium for this non-linear kinetic model by hypocoercivity estimates. Th…
Trend to equilibrium and hypoelliptic regularity for the relativistic Fokker-Planck equation
Anton Arnold, Gayrat Toshpulatov
We consider the relativistic, spatially inhomogeneous Fokker-Planck equation with an external confining potential. We prove the exponential time decay of solutions towards the glob…