Similarity reduction of energy-transport models for semiconductors

Abstract

The main purpose of this work is to perform symmetry classification of a system of partial differential equations for energy-transport in semiconductors. In the case where there are symmetries, they are used to reduce the number of independent variables which in turn enables one to construct invariant solutions. Invariant solutions of a given equation satisfy an equation with fewer independent variables. Thus, the search of invariant solutions can be viewed as a sort of dimensional reduction. From a computational standpoint, the reduced system is easier to analyse both numerically and analytically than the original system.