STEADY-STATE SOLUTIONS AND ASYMPTOTIC LIMITS ON THE MULTI-DIMENSIONAL SEMICONDUCTOR QUANTUM HYDRODYNAMIC MODEL

DOI10.1142/S0218202507001905zbMath1202.82091MaRDI QIDQ5293960

Bo Liang, Kai-Jun Zhang

Publication date: 5 July 2007

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

existence and uniquenessquantum hydrodynamicsasymptotic limits

Mathematics Subject Classification ID

Boundary value problems for nonlinear higher-order PDEs (35G30) PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of semiconductors (82D37) Hypersonic flows (76K05) Euler-Poisson-Darboux equations (35Q05)

Related Items

On the bipolar multidimensional quantum Euler--Poisson system: the thermal equilibrium solution and semiclassical limit, Positive solutions to a nonlinear fourth-order partial differential equation, Long-time self-similarity of classical solutions to the bipolar quantum hydrodynamic models, Asymptotic stability of nonlinear diffusion waves for the bipolar quantum Euler–Poisson system with time‐dependent damping, UNIFORM CONVERGENT MULTIGRID METHODS FOR ELLIPTIC PROBLEMS WITH STRONGLY DISCONTINUOUS COEFFICIENTS, The stationary solution of a one-dimensional bipolar quantum hydrodynamic model, Exponential decay to a quantum hydrodynamic model for semiconductors, Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors, Existence of the solution for the viscous bipolar quantum hydrodynamic model, Quasineutral limit of bipolar quantum hydrodynamic model for semiconductors, Mathematical analysis to a nonlinear fourth-order partial differential equation, The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors, Global solutions for the compressible quantum hydrodynamic model in a bounded domain, Large-time behavior of solutions to the bipolar quantum Euler-Poisson system with critical time-dependent over-damping, Global existence and large time behavior of solutions for the bipolar quantum hydrodynamic models in the quarter plane

Cites Work

• Thermal equilibrium states of the quantum hydrodynamic model for semiconductors in one dimension
• The quantum hydrodynamic model for semiconductors in thermal equilibrium
• Existence and asymptotic behavior of multi-dimensional quantum hydrodynamic model for semiconductors
• Nonlinear problems in quantum semiconductor modeling.
• Elliptic Partial Differential Equations of Second Order
• ASYMPTOTIC LIMITS FOR QUANTUM TRAJECTORY MODELS
• Quantum Euler-Poisson systems: global existence and exponential decay
• Analysis of the viscous quantum hydrodynamic equations for semiconductors
• LOCAL EXISTENCE OF SOLUTIONS TO THE TRANSIENT QUANTUM HYDRODYNAMIC EQUATIONS
• On a steady-state quantum hydrodynamic model for semiconductors
• Positive solutions to singular second and third order differential equations for quantum fluids