Existence and Stability of Stationary Solutions with Boundary Layers in a Tikhonov-Type System Arising in the Drift-Diffusion Model of Semiconductors of Sub-Debye-Length

IF 1.9 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2026-01-26 DOI:10.1134/S1061920825601533

A.V. Karamyshev, E.I. Nikulin

引用次数: 0

Abstract

This paper investigates stationary boundary-layer solutions of singularly perturbed systems of Tikhonov-type equations arising in drift-diffusion models of sub-Debye semiconductors. Boundary-layer asymptotics for solutions are constructed for Neumann and Dirichlet boundary conditions. The asymptotic method of differential inequalities is used to prove the existence and asymptotic stability theorems for these solutions. A physical interpretation of the results thus obtained is provided.

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亚德拜长度半导体漂移扩散模型中tikhonov型系统边界层平稳解的存在性与稳定性

本文研究了亚debye半导体漂移扩散模型中奇异摄动系统tikhonov型方程的平稳边界层解。构造了Neumann和Dirichlet边界条件下解的边界层渐近性。利用微分不等式的渐近方法证明了这些解的存在性和渐近稳定性定理。本文提供了对所得结果的物理解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.