Theory of orthogonality of eigenfunctions of the characteristic equations as a method of solution boundary problems for model kinetic equations

2014/07/28 by А. В. Латышев, Latyshev, A. V., Alexander D. Kurilov +1
Engineering · Mathematics · #81 A 20 #81 A 40 #81 A 99 #Combustion and Detonation Processes #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1407.7345

openalex publication_date 2014/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann boundary value problem with a coefficient equal to the ratio of the boundary values dispersion function, develops the theory of the half-space orthogonality of generalized singular eigenfunctions corresponding characteristic equations, which leads separation of variables. And in this two boundary value problems of the kinetic theory (diffusion light component of a binary gas and Kramers problem about isothermal slip) shows the application of the theory orthogonality eigenfunctions for analytical solutions these tasks.

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