Communications in Mathematical Sciences
Volume 14 (2016)
Asymptotic stability and semi-classical limit for bipolar quantum hydrodynamic model
Pages: 2331 – 2371
In this paper, the initial-boundary value problem of a 1-D bipolar quantum semiconductor hydrodynamic model is investigated under a non-linear boundary condition which means the quantum effect vanishes on the boundary. First of all, the existence and uniqueness of the corresponding stationary solution are established. Then the exponentially asymptotic stability of the stationary solution and the semi-classical limits are further studied. The adopted approach is the elementary energy method but with some new developments.
bipolar quantum hydrodynamic model, stationary solution, energy estimates, asymptotic stability, semi-classical limit
2010 Mathematics Subject Classification
35A01, 35B35, 35B40, 35B45, 35M33, 82D37