2012/06/25 by Ansgar Jüngel, Jüngel, Ansgar, René Pinnau +3
Mathematics · #35K20 #35Q70 #82D37 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods for differential equations #math.AP #msc:35K20 #msc:35Q70 #msc:82D37
paper · pdf · doi:10.48550/arxiv.1206.5722
arxiv created 2012/06/25 · openalex publication_date 2012/06/25 · arxiv updated 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simplified transient energy-transport system for semiconductors subject to\nmixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally\nderived from the non-isothermal hydrodynamic equations in a particular\nvanishing momentum relaxation limit. It consists of a drift-diffusion-type\nequation for the electron density, involving temperature gradients, a nonlinear\nheat equation for the electron temperature, and the Poisson equation for the\nelectric potential. The global-in-time existence of bounded weak solutions is\nproved. The proof is based on the Stampacchia truncation method and a careful\nuse of the temperature equation. Under some regularity assumptions on the\ngradients of the variables, the uniqueness of solutions is shown. Finally,\nnumerical simulations for a ballistic diode in one space dimension illustrate\nthe behavior of the solutions.\n