Semiclassical limit in a simplified quantum energy-transport model for semiconductors
Abstract
The semiclassical limit in a quantum energy-transport model for semiconductorsis proved. The system consists of a nonlinear parabolic fourth-order equationfor the electron density, including temperature gradients; a degenerate ellipticheat equation for the electron temperature; and the Poisson equation for theelectric potential. The equations are solved in a bounded domain with periodicboundary conditions. The asymptotic limit is based on a priori estimates independentof the scaled Planck constant, obtained from entropy functionals, on theuse of Gagliardo-Nirenberg inequalities, and weak compactness methods.
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