References
- Hu H, Zhang K. Semiconductor full quantum hydrodynamic model with non-flat doping profile: (I) stability; 2021, submitted.
- Gardner CL. The quantum hydrodynamic model for semiconductor devices. SIAM J Appl Math. 1994;54:409–427.
- Gardner CL. Resonant tunneling in the quantum hydrodynamic model. VLSI Des. 1995;3:201–210.
- Markowich PA, Ringhofer CA, Schmeiser C. Semiconductor equations. Vienna: Springer-Verlag; 1990.
- Zhang K, Hu H. Introduction to semiconductor partial differential equations (Chinese edition). Beijing: Science Press; 2016.
- Nishibata S, Suzuki M. Initial boundary value problems for a quantum hydrodynamic model of semiconductors: asymptotic behaviors and classical limits. J Differ Equ. 2008;244:836–874.
- Hu H, Mei M, Zhang K. Asymptotic stability and semi-classical limit for bipolar quantum hydrodynamic model. Commun Math Sci. 2016;14:2331–2371.
- Huang F, Li H, Matsumura A. Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors. J Differ Equ. 2006;225:1–25.
- Di Michele F, Mei M, Rubino B, Sampalmieri R. Stationary solutions to hybrid quantum hydrodynamical model of semiconductors in bounded domain. Int J Numer Anal Model. 2016;13:898–925.
- Di Michele F, Mei M, Rubino B, Sampalmieri R. Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time. Math Mech Solids. 2019;24:2096–2115.
- Unterreiter A. The thermal equilibrium solution of a generic bipolar quantum hydrodynamic model. Commun Math Phys. 1997;188:69–88.
- Di Michele F, Mei M, Rubino B, Sampalmieri R. Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics. J Differ Equ. 2017;263:1843–1873.
- Zhang G, Li H, Zhang K. Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors. J Differ Equ. 2008;245:1433–1453.
- Pu X, Guo B. Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction. Kinet Relat Models. 2016;9:165–191.
- Pinnau R. A note on boundary conditions for quantum hydrodynamic equations. Appl Math Lett. 1999;12:77–82.
- Nishibata S, Suzuki M. Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors. Arch Rational Mech Anal. 2009;192:187–215.