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<p>This paper is a survey of results concerning asymptotics of solutions of singularly perturbed systems of transport equations; it also contains some new results. We discuss the so-called critical problems whose degenerate solutions are one-parameter families. Under certain conditions, this leads to a fast establishment of dynamic equilibrium between the components of the solution and the subsequent transfer with an “average” speed. The domains of large gradients of the initial conditions generate inner layers, which can be described by linear parabolic equations and their generalizations, for example, equations of the Burgers and Burgers–Korteweg–de&#xa0;Vries types.</p>

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ON THE ASYMPTOTICS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR A SINGULARLY PERTURBED SYSTEM OF TRANSFER EQUATIONS WITH WEAK NONLINEAR DIFFUSION

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. V. Nesterov

摘要

This paper is a survey of results concerning asymptotics of solutions of singularly perturbed systems of transport equations; it also contains some new results. We discuss the so-called critical problems whose degenerate solutions are one-parameter families. Under certain conditions, this leads to a fast establishment of dynamic equilibrium between the components of the solution and the subsequent transfer with an “average” speed. The domains of large gradients of the initial conditions generate inner layers, which can be described by linear parabolic equations and their generalizations, for example, equations of the Burgers and Burgers–Korteweg–de Vries types.