Viscous quantum hydrodynamics and parameter-elliptic systems

DOI10.1002/mma.1377zbMath1211.35044OpenAlexW2008102191MaRDI QIDQ3168665

Li Chen, Michael Dreher

Publication date: 19 April 2011

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

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-191454

zbMATH Keywords

exponential stabilityanalytic semigroupdecay ratesemiconductor modelShapiro-Lopatinskii criterion

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Statistical mechanics of semiconductors (82D37)

Related Items (8)

The full viscous quantum hydrodynamic system in one dimensional space ⋮ Quantum Semiconductor Models ⋮ Global existence of the three-dimensional viscous quantum magnetohydrodynamic model ⋮ Resolvent estimates for Douglis-Nirenberg systems ⋮ Stability of a one-dimensional full viscous quantum hydrodynamic system ⋮ Large data solutions to the viscous quantum hydrodynamic model with barrier potential ⋮ The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential ⋮ Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations

Cites Work

• Existence of weak solution and semiclassical limit for quantum drift-diffusion model
• The existence and long-time behavior of weak solution to bipolar quantum drift-diffusion model
• The Dirichlet problem of the quantum drift-diffusion model
• Global existence of solutions to one-dimensional viscous quantum hydrodynamic equations
• Exponential decay in time of solutions of the viscous quantum hydrodynamic equations
• Quantum energy-transport and drift-diffusion models
• Physical and numerical viscosity for quantum hydrodynamics
• Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
• A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
• Interior estimates for elliptic systems of partial differential equations
• Convergent semidiscretization of a nonlinear fourth order parabolic system
• Quantum Euler-Poisson systems: global existence and exponential decay
• On a steady-state quantum hydrodynamic model for semiconductors
• THE VISCOUS MODEL OF QUANTUM HYDRODYNAMICS IN SEVERAL DIMENSIONS
• The transient equations of viscous quantum hydrodynamics
• Eigenvalue asymptotics for a boundary problem involving an elliptic system
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II

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