ENERGY-TRANSPORT LIMIT OF THE HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

Abstract

This paper is mainly devoted to study the energy-transport limit of a non-isentropic hydrodynamic model with momentum relaxation time τ and energy relaxation time σ. Inspired by the Maxwell iteration, we construct a new approximation under the assumption τσ = 1, and show that periodic initial-value problems of a certain scaled hydrodynamic model have unique smooth solutions in a finite time interval independent of τ. Furthermore, it is also obtained that as τ tends to zero, the smooth solutions converge to the smooth solutions of energy-transport models at the rate of τ2. The proof of these results is based on a continuation principle.