2020/02/17 by Toru Kan, Masahiro Suzuki, Kan, Toru +1
Computer Science · Engineering · Mathematics · #35B10 #35B35 #35B40 #35B45 #82D37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2002.06872
openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main purpose of this paper is mathematical analysis on time-periodic flows of electrons and holes in semiconductors. The flows appear in a situation that alternating-current voltages are applied to devices. In this paper, we study the drift-diffusion model for semiconductors in a three-dimensional bounded domain and investigate the existence and stability of time-periodic solutions. We first derive the uniform-in-time estimate of time-global solutions, and then prove by the relative entropy method that the difference of any two solutions decays exponentially fast as time tends to infinity. These facts enable us to show the unique existence and global stability of time-periodic solution.