Hypocoercivity for the non-linear semiconductor Boltzmann equation

2024/11/17 by Marlies Pirner, Pirner, Marlies, Gayrat Toshpulatov +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #35B40 #35Q20 #35Q81 #35Q82 #82C40 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2411.11023

openalex publication_date 2024/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. This seems to be the first hypocoercivity result for this nonlinear kinetic equation for semiconductor devices without smallness assumptions. The analysis benefits from uniform bounds of the solution in terms of the equilibrium velocity distribution.

Cited by

• Conditional hypocoercivity for nonlinear kinetic Fokker--Planck equations
• Long time behavior of discrete velocity kinetic equations

Related

• Hypocoercivity for the Linear Semiconductor Boltzmann Equation with Boundaries and Uncertainties
• Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
• Hypocoercivity for linear kinetic equations conserving mass
• Hypocoercivity without confinement
• Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation without Angular Cutoff