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math.AP2024
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…
math.AP2024
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…