On a drift-diffusion system for semiconductor devices

TL;DR

This paper analyzes a fractional Poisson-Nernst-Planck model for semiconductors, establishing decay estimates in various dimensions and deriving the leading term of its long-term asymptotic expansion.

Contribution

It introduces decay estimates and asymptotic expansion results for a fractional PDE model of semiconductor devices, advancing understanding of their long-term behavior.

Findings

Decay estimates for Lebesgue and Sobolev norms in 1D, 2D, and 3D

First term of the asymptotic expansion as time approaches infinity

Insights into the long-term dynamics of fractional semiconductor models

Abstract

In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two and three dimensions. We also provide the first term of the asymptotic expansion as $t\rightarrow\infty$.