一维稳态量子能量输运模型的古典解
Classical solutions to stationary one-dimensional quantum energy-transport model

摘要： 在一维有界区域上研究一个半导体量子能量输运稳态模型,在热导率依赖于电子密度和电子温度的情形下,证明了其古典解的存在性。另外,当晶格温度充分大且电子密度相对较小时证明了其解的唯一性。 证明利用指数变换、Leray-Schauder不动点定理和一些不等式技巧。
Abstract: A stationary quantum energy-transport model for semiconductors was studied in a one-dimensional bounded domain. The existence of classical solutions was proved in the case that the heat conductivity depends on the electron density and the electron temperature. Moreover, the uniqueness of the solutions was shown when the lattice temperature was large enough and the current density was relatively small. The proof was based on using an exponential variable transformation, the Leray-Schauder fixed-point theorem and some inequality techniques