Application of the similarity method to the nonlinear Boltzmann equation

DOI10.1007/BF00952113zbMath0553.76066OpenAlexW2052523277MaRDI QIDQ759586

Theo F. Nonnenmacher

Publication date: 1984

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00952113

zbMATH Keywords

nonlinear Boltzmann equationspatially homogeneousarbitrary source termexact similarity solutionsgroup-theoretic technique

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items (11)

Similarity analysis and exact solutions for a general discrete two- velocity model of Boltzmann equation ⋮ 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 ⋮ Exact solutions of the Boltzmann equations with a source ⋮ New classes of similarity solutions for the nonlinear Carleman-Boltzmann equation ⋮ Exact similarity solutions for nonlinear particle transport in a host medium ⋮ Revisiting diffusion: Self-similar solutions and the 𝑡^{-1/2} decay in initial and initial-boundary value problems ⋮ L\({}^ 1\)-stability of the solutions to an integral evolution equation of the non-linear particle transport theory ⋮ Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential ⋮ Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term ⋮ Group properties of equations of the kinetic theory of coagulation

Cites Work

• Unnamed Item
• Some classes of exact solutions of the nonlinear Boltzmann equation

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