Weak solutions to isothermal hydrodynamic model for semiconductor devices

DOI10.1016/j.jde.2009.07.032zbMath1180.82204OpenAlexW2071238613MaRDI QIDQ1039761

Huimin Yu, Tian-Hong Li, Fei-Min Huang

Publication date: 23 November 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.07.032

zbMATH Keywords

entropysemiconductorcompensated compactnessisothermal Euler-Poisson equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Statistical mechanics of semiconductors (82D37) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Motion of charged particles (78A35)

Related Items (21)

Weak solutions to the Cauchy problem of the time-dependent Thomas–Fermi equations ⋮ Large time behavior of solutions to a bipolar hydrodynamic model with big data and vacuum ⋮ Existence and asymptotic behavior of smooth solutions to bipolar hydrodynamic model ⋮ Global solutions of the Cauchy problem to Euler-Poisson equations of two-carrier types ⋮ Uniformly time-independent \(L^\infty\) estimate for a one-dimensional hydrodynamic model of semiconductors ⋮ Global solutions and relaxation limit to the Cauchy problem of a hydrodynamic model for semiconductors ⋮ Uniform boundedness in weak solutions to a specific dissipative system ⋮ Large-time behavior of entropy solutions to bipolar hydrodynamic model for semiconductors ⋮ From gas dynamics with large friction to gradient flows describing diffusion theories ⋮ Stability of steady states of the compressible Euler-Poisson system in \(\mathbb R^3\) ⋮ Multi-dimensional bipolar hydrodynamic model of semiconductor with insulating boundary conditions and non-zero doping profile ⋮ Existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices with variable coefficient damping ⋮ Zero relaxation time limits to isothermal hydrodynamic model for semiconductor ⋮ Uniform boundedness in time and large time behavior of weak solutions to a kind of dissipative system ⋮ On the isothermal compressible Euler equations with frictional damping ⋮ Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices ⋮ Relaxation limit in bipolar semiconductor hydrodynamic model with non-constant doping profile ⋮ Isometric Immersion of Surface with Negative Gauss Curvature and the Lax--Friedrichs Scheme ⋮ Large time behavior of Euler-Poisson equations for isothermal fluids with spherical symmetry ⋮ Large time behavior of solutions to multi-dimensional bipolar hydrodynamic model of semiconductors with vacuum ⋮ Large-time behavior of the full compressible Euler-Poisson system without the temperature damping

Cites Work

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• Convergence of the viscosity method for isentropic gas dynamics
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• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations
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• Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation
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• Convergence of Viscosity Solutions for Isothermal Gas Dynamics
• Global solution for an initial boundary value problem of a quasilinear hyperbolic system
• Solutions in the large for some nonlinear hyperbolic conservation laws
• Asymptotics of initial boundary value problems for hydrodynamic and drift diffusion models for semiconductors

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