Singular solutions of the Vlasov-Maxwell system on a half line

DOI10.1007/BF00382888zbMath0840.76097OpenAlexW1986868965MaRDI QIDQ1905659

Yan Guo

Publication date: 10 January 1996

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00382888

zbMATH Keywords

boundary conditionsVlasov-Poisson systemregularity of solutionspartial absorptionpurely specular reflection

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Statistical mechanics of plasmas (82D10) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)

Related Items (36)

BV-regularity of the Boltzmann equation in non-convex domains ⋮ On quantitative hypocoercivity estimates based on Harris-type theorems ⋮ The Lagrangian structure of the Vlasov-Poisson system in domains with specular reflection ⋮ Linear stability of the Vlasov-Poisson system with boundary conditions ⋮ On global existence for the Vlasov-Poisson system in a half space ⋮ On the structure of the singular set for the kinetic Fokker–Planck equations in domains with boundaries ⋮ Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus ⋮ On a Vlasov-Poisson system in a bounded set with direct reflection boundary conditions ⋮ Lipschitz continuous solutions of the Vlasov-Maxwell systems with a conductor boundary condition ⋮ Energy conservation of the DiPerna-Lions solutions to Vlasov-Maxwell systems ⋮ Global well-posedness of Vlasov-Poisson-type systems in bounded domains ⋮ Nonuniqueness for the kinetic Fokker-Planck equation with inelastic boundary conditions ⋮ Formation and propagation of discontinuity for Boltzmann equation in non-convex domains ⋮ Uniqueness for weak solutions of a one-dimensional boundary value problem for the Vlasov-Poisson system ⋮ Instantaneous filling of the vacuum for the full Boltzmann equation in convex domains ⋮ The Fokker--Planck Equation with Absorbing Boundary Conditions in Bounded Domains ⋮ Weak solutions for the Vlasov-Poisson initial-boundary value problem with bounded electric field ⋮ Regularity of the Boltzmann equation in convex domains ⋮ Global classical solution to the Navier-Stokes-Vlasov equations with large initial data and reflection boundary conditions ⋮ Global existence for the Vlasov-Poisson system in bounded domains ⋮ The Cauchy problem for the 3-D Vlasov-Poisson system with point charges ⋮ Decay and continuity of the Boltzmann equation in bounded domains ⋮ Analysis of the relativistic Vlasov-Maxwell model in an interval ⋮ Global magnetic confinement for the 1.5D Vlasov-Maxwell system ⋮ The Fokker-Planck equation with absorbing boundary conditions ⋮ Onsager-type conjecture and renormalized solutions for the relativistic Vlasov–Maxwell system ⋮ Existence and BV-Regularity for Neutron Transport Equation in NonConvex Domain ⋮ Regularity of Boltzmann Equation with External Fields in Convex Domains of Diffuse Reflection ⋮ \(L^2\) solution of linear non-cutoff Boltzmann equation with boundary conditions ⋮ SINGULARITIES OF STATIONARY SOLUTIONS TO THE VLASOV–POISSON SYSTEM IN A POLYGON ⋮ Smooth steady solutions of the planar Vlasov-Poisson system with a magnetic obstacle ⋮ Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition ⋮ The Boltzmann Equation in Bounded Domains ⋮ Stationary solutions of the Vlasov-Poisson system with diffusive boundary conditions ⋮ The Vlasov-Poisson-Landau system with the specular-reflection boundary condition ⋮ Mean field limit for the one dimensional Vlasov-Poisson~equation

Cites Work

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• Singularity formation in a collisionless plasma could occur only at high velocities
• Boundary value problems in abstract kinetic theory
• Abstract time-dependent transport equations
• Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data
• Boundary value problems for the Vlasov-Maxwell equation in one dimension
• Global weak solutions of the Vlasov-Maxwell system with boundary conditions
• A boundary‐value problem for the stationary vlasov‐poisson equations: The plane diode

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