Hypocoercivity for the non-linear semiconductor Boltzmann equation

TL;DR

This paper proves exponential decay to equilibrium for a nonlinear semiconductor Boltzmann equation using hypocoercivity, marking the first such result without smallness assumptions, and relies on uniform bounds of the solution.

Contribution

It provides the first hypocoercivity proof for a nonlinear kinetic semiconductor model without smallness constraints.

Findings

Exponential decay to equilibrium established.

Uniform bounds of the solution are crucial.

First hypocoercivity result for this nonlinear model.

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.