Asymptotics of solving a singularly perturbed system of transport equations with fast and slow components in the critical case

2023/08/21 by Andrey Nesterov, Nesterov, Andrey
Computer Science · Mathematics · #35C20 (Primary) 35F35 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2308.10670

openalex publication_date 2023/08/21 · openalex created_date 2023/08/23 · openalex updated_date 2026/07/28

Abstract

An asymptotic expansion with respect to a small parameter of the solution of the Cauchy problem is constructed for a system of three transfer equations, two of which are singularly perturbed by the degeneracy of the entire senior part of the transfer operator, and the third equation clearly does not contain a small parameter. The peculiarity of the problem is that it belongs to the so-called critical case: the solution of a degenerate problem is a one-parameter family. The asymptotic expansion of the solution under smooth initial conditions is constructed as the sum of the regular part and boundary functions.

Related

• To substantiate the asymptotics of solving the Cauchy problem for a singularly perturbed weakly nonlinear transport equation
• A singularly perturbed system of parabolic equations
• Computational aspects of finding a solution asymptotics for a singularly\n perturbed system of differential equations
• Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions
• Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations