On the Cauchy problem for Wigner-Poisson-BGK equation in the Wiener algebra

DOI10.1002/mma.3510zbMath1339.35259OpenAlexW1605668383MaRDI QIDQ2802663

Bin Li, Jie-qiong Shen

Publication date: 26 April 2016

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

Full work available at URL: https://doi.org/10.1002/mma.3510

zbMATH Keywords

mild solutionWiener algebraWigner-Poisson-BGK

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Nonlinear evolution equations (47J35)

Cites Work

• Unnamed Item
• Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
• On the BGK equation with some force fields in \(L^p\) space
• The Cauchy problem for the BGK equation with an external force
• On the Cauchy problem of the Vlasov-Poisson-BGK system: global existence of weak solutions
• The BGK model with external confining potential: existence, long-time behaviour and time-periodic Maxwellian equilibria
• Diffusive corrections to asymptotics of a strong-field quantum transport equation
• Semigroups of linear operators and applications to partial differential equations
• A mathematical analysis of quantum transport in three-dimensional crystals
• Weighted \(L^ \infty\) bounds and uniqueness for the Boltzmann BGK model
• Global \(L^{1}\) theory and regularity for the 3D nonlinear Wigner-Poisson-Fokker-Planck system.
• An analysis of quantum Fokker-Planck models: a Wigner function approach
• Global weak solutions to the Vlasov-Poisson-BGK system for initial data in \(L^p(\mathbb R^3{\times}\mathbb R^3)\)
• On the three-dimensional Wigner--Poisson problem with inflow boundary conditions
• The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive effects
• Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations
• Strichartz Estimates for the Kinetic Transport Equation
• On the equivalence of the Schrödinger and the quantum Liouville equations
• L p solutions to the Cauchy problem of the BGK equation
• Short Pulses Approximations in Dispersive Media
• The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
• The Wigner Poisson Problem in a Crystal: Existence, Uniqueness, Semiclassical Limit in the One-dimensional Case
• Existence, uniqueness and asymptotic behavior of Wigner-Poisson and Vlasov-Poisson systems: A survey
• An Operator Splitting Method for the Wigner–Poisson Problem
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems

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