Global solution to a nonlinear integral evolution problem in particle transport theory

DOI10.1063/1.525309zbMath0507.70011OpenAlexW1987527693MaRDI QIDQ4745317

Vinicio C. Boffi, Giampiero Spiga

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525309

zbMATH Keywords

velocity distributionglobal existence and uniquenesscontracting mapping principlenonlinear integral evolution equationsscattering probability distribution

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Transport processes in time-dependent statistical mechanics (82C70) (n)-body problems (70F10) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items (8)

On a nonlinear evolution problem of particle transport theory with nonconstant collision frequencies ⋮ Particle transport in a host medium with an external source: Exact solutions for a nonlinear homogeneous Boltzmann equation ⋮ \(L^ 2\)-stability near equilibrium of the solution of the homogeneous Boltzmann equation in the case of Maxwellian molecules ⋮ L\({}^ 1\)-stability of the solutions to an integral evolution equation of the non-linear particle transport theory ⋮ Global solutions and \(L^ 1\)-stability to a nonlinear evolution problem in the diffusion of the particles of a mixture ⋮ Some rigorous results in nonlinear particle transport theory ⋮ Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term ⋮ Nonlinear evolution problems in the diffusion of the particles of a mixture

Cites Work

• A non-standard approach to the Boltzmann equation
• The Boltzmann equation. I. Uniqueness and local existence
• Sur la théorie de l'équation intégrodifferentielle de Boltzmann
• Rigorous iterated solutions to a nonlinear integral evolution problem in particle transport theory

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