Existence and Stability of Time-periodic Solutions to the Drift-diffusion Model for Semiconductors
by Toru Kan   Masahiro Suzuki  

Vol. 10 No. 4 (2015) P.615~P.638

ABSTRACT

We study the existence and the asymptotic stability of time-periodic solutions to the driftdiffusion model for semiconductors. If alternating-current voltage is applied to PN-junction diodes, a time-periodic current flow is observed. The main purpose of the present paper is mathematical analysis on this periodic flow. We construct a time-periodic solution by utilizing the Galerkin method. The solution is unique in a neighborhood of a thermal equilibrium, and it is globally stable. Proofs of the uniqueness and the stability are based on the energy method employing an energy form.

KEYWORDS
drift-diffusion model; time-periodic solution; global stability

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35B10; 35B35; 35B40; 82D37

MILESTONES

Received: 2015-03-30
Revised : 2015-06-17
Accepted: 2015-06-16

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