Semiconductor full quantum hydrodynamic model with non-flat doping profile. I: Stability of steady state. (English) Zbl 1527.35420
Summary: This is the first part of our series of studies concerning the full quantum hydrodynamic model for semiconductors with non-flat doping profile. In this paper, we are concerned with the existence, uniqueness and asymptotic stability of subsonic steady states to the model in a bounded interval, which is subject to physical boundary conditions. The main results are proved by Stampacchia’s truncation method, the Leray-Schauder Fixed Point Theorem, Schauder’s Fixed Point Theorem and intricate energy estimates.
MSC:
35Q81 | PDEs in connection with semiconductor devices |
82D37 | Statistical mechanics of semiconductors |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
35B35 | Stability in context of PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
35M33 | Initial-boundary value problems for mixed-type systems of PDEs |
76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
76G25 | General aerodynamics and subsonic flows |
47H10 | Fixed-point theorems |