8 papers · 1 filter
Well-posedness for the spatially inhomogeneous Fermi-Dirac-Fokker-Planck equation
Gayrat Toshpulatov
This paper is concerned with the spatially inhomogeneous Fermi-Dirac-Fokker-Planck equation posed on a classical kinetic phase space. The nonlinear factor appears both in…
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…
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…
Well-posedness and trend to equilibrium for the Vlasov-Poisson-Fokker-Planck system with a confining potential
Gayrat Toshpulatov
We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution o…
Exponential stability and hypoelliptic regularization for the kinetic Fokker-Planck equation with confining potential
Anton Arnold, Gayrat Toshpulatov
This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker-Planck equations with non-quadr…