On the initial boundary-value problem for the Vlasov-Poisson system: Existence of weak solutions and stability

DOI10.1007/BF00375153zbMath0828.76097MaRDI QIDQ1894121

Jürgen Weckler

Publication date: 15 January 1996

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

zbMATH Keywords

boundary conditionsCoulomb potentialbounded domaincompactness argumentmeasure preserving floweffects of reflectionsenergy- Casimir method

Mathematics Subject Classification ID

Statistical mechanics of plasmas (82D10) Partial differential equations of mathematical physics and other areas of application (35Q99) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)

Related Items (10)

Classical solutions of the Vlasov-Poisson equations with external magnetic field in a half-space ⋮ The Lagrangian structure of the Vlasov-Poisson system in domains with specular reflection ⋮ On a Vlasov-Poisson system in a bounded set with direct reflection boundary conditions ⋮ CONVERGENCE OF A hp-STREAMLINE DIFFUSION SCHEME FOR VLASOV–FOKKER–PLANCK SYSTEM ⋮ On the existence of global compactly supported weak solutions of the Vlasov-Poisson system with an external magnetic field ⋮ A priori estimate of solutions of a mixed problem for the Vlasov-Poisson system with a homogeneous external magnetic field ⋮ Global well-posedness of Vlasov-Poisson-type systems in bounded domains ⋮ Initial-boundary value problems for the Vlasov-Poisson equations in a half-space ⋮ On the unique solvability of initial boundary value problems for the Vlasov-Poisson system of equations in a half-space ⋮ Stationary solutions of the Vlasov equations for a high-temperature two-component plasma

Cites Work

• The Green function for uniformly elliptic equations
• A rigorous stability result for the Vlasov-Poisson system in three dimensions
• Global weak solutions of the Vlasov-Maxwell system with boundary conditions
• Ein Existenzbeweis für die Vlasov-Gleichung der Stellardynamik bei gemittelter Dichte
• An existence theorem for the unmodified Vlasov Equation
• Weak solutions of the Vlasov-Poisson initial boundary value problem
• Weak solutions of the initial value problem for the unmodified non‐linear vlasov equation
• Existence of stationary, collisionless plasmas in bounded domains
• Elliptic Partial Differential Equations of Second Order
• Weak solutions of the initial‐boundary value problem for the Vlasov–Poisson system
• Non‐linear stability for the Vlasov–Poisson system—the energy‐Casimir method
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