The Dirichlet problem of the quantum drift-diffusion model

DOI10.1016/j.na.2007.09.003zbMath1158.35372OpenAlexW1978552484MaRDI QIDQ949737

Li Chen, Xiu-Qing Chen, Huai-Yu Jian

Publication date: 21 October 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.09.003

zbMATH Keywords

weak solutionsemi-discretizationfourth order parabolic systemglobal regular weak solutionsnew entropy estimate

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Initial-boundary value problems for higher-order parabolic equations (35K35) PDEs in connection with quantum mechanics (35Q40)

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Cites Work

• Semiclassical limit for bipolar quantum drift-diffusion model
• Existence of weak solution and semiclassical limit for quantum drift-diffusion model
• The semiclassical limit in the quantum drift-diffusion equations with isentropic pressure
• Existence, semiclassical limit and long-time behavior of weak solution to quantum drift-diffusion model
• Compact sets in the space \(L^ p(0,T;B)\)
• On the stationary quantum drift-diffusion model
• Exponential time decay of solutions to a nonlinear fourth-order parabolic equation
• Quantum energy-transport and drift-diffusion models
• Nonlinear problems in quantum semiconductor modeling.
• Global Nonnegative Solutions of a Nonlinear Fourth-Order Parabolic Equation for Quantum Systems
• A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
• Existence and positivity of solutions of a fourth‐order nonlinear PDE describing interface fluctuations
• Convergent semidiscretization of a nonlinear fourth order parabolic system
• Quantum Euler-Poisson systems: global existence and exponential decay
• A REVIEW ON THE QUANTUM DRIFT DIFFUSION MODEL
• Long-time behavior for a nonlinear fourth-order parabolic equation
• THE VISCOUS MODEL OF QUANTUM HYDRODYNAMICS IN SEVERAL DIMENSIONS

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