Asymptotic stability and semi-classical limit for bipolar quantum hydrodynamic model

DOI10.4310/CMS.2016.V14.N8.A10zbMath1356.35248OpenAlexW2545230984MaRDI QIDQ346011

Ming Mei, Kai-Jun Zhang, Hai-feng Hu

Publication date: 5 December 2016

Published in: Communications in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/cms.2016.v14.n8.a10

zbMATH Keywords

energy estimatesasymptotic stabilitystationary solutionsemi-classical limitbipolar quantum hydrodynamic model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) A priori estimates in context of PDEs (35B45) Statistical mechanics of semiconductors (82D37) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Initial-boundary value problems for mixed-type systems of PDEs (35M33) PDEs in connection with statistical mechanics (35Q82)

Related Items (9)

Semiconductor full quantum hydrodynamic model with non-flat doping profile: (II) semi-classical limit ⋮ Existence and uniqueness of steady states to semiconductor bipolar full quantum hydrodynamic model ⋮ Asymptotic stability of nonlinear diffusion waves for the bipolar quantum Euler–Poisson system with time‐dependent damping ⋮ The stationary solution of a one-dimensional bipolar quantum hydrodynamic model ⋮ The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors ⋮ Relaxation limit in bipolar semiconductor hydrodynamic model with non-constant doping profile ⋮ Large-time behavior of solutions to the bipolar quantum Euler-Poisson system with critical time-dependent over-damping ⋮ Large-time behavior of solutions to the bipolar quantum Navier-Stokes-Poisson equations ⋮ Asymptotic stability of the stationary wave for the quantum Navier-Stokes-Poisson system

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