Existence, semiclassical limit and long-time behavior of weak solution to quantum drift-diffusion model

DOI10.1016/j.nonrwa.2008.01.008zbMath1171.35329OpenAlexW2038454875MaRDI QIDQ1015046

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

Publication date: 7 May 2009

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2008.01.008

zbMATH Keywords

weak solutionlogarithmic Sobolev inequalitylong-time behaviorsemiclassical limitone space dimensionquantum drift-diffusion modelentropy estimatesemi-discretization in timeelliptic parabolic system

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with optics and electromagnetic theory (35Q60) Initial-boundary value problems for higher-order parabolic equations (35K35) Singular perturbations in context of PDEs (35B25) PDEs in connection with quantum mechanics (35Q40)

Related Items

Quantum Semiconductor Models, A simplified quantum energy-transport model for semiconductors, Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors., The existence and long-time behavior of weak solution to bipolar quantum drift-diffusion model, The Dirichlet problem of the quantum drift-diffusion model, ASYMPTOTIC BEHAVIORS AND CLASSICAL LIMITS OF SOLUTIONS TO A QUANTUM DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS, The semiclassical limit in the quantum drift-diffusion model

Cites Work

• Existence of weak solution and semiclassical limit for 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
• Analysis of a Multidimensional Parabolic Population Model with Strong Cross-Diffusion
• 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