论多个空间变量情况下具有弱扩散性的奇异扰动算子-微分传输方程的考希问题解的渐近性

Pub Date : 2024-04-22 DOI:10.1134/s0965542524030114

A. V. Nesterov

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引用次数: 0

摘要

摘要在多个空间变量的情况下，为具有小非线性和弱扩散性的奇异扰动算子微分输运方程的考希问题解构建了形式化的渐近展开。在对问题数据施加的条件下，前导渐近项由多维广义伯格斯-科特韦格-德弗里斯方程描述。在某些条件下，余数是根据残差估算的。

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On Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator-Differential Transport Equation with Weak Diffusion in the Case of Several Space Variables

Abstract

A formal asymptotic expansion is constructed for the solution of the Cauchy problem for a singularly perturbed operator differential transport equation with small nonlinearities and weak diffusion in the case of several space variables. Under the conditions imposed on the data of the problem, the leading asymptotic term is described by the multidimensional generalized Burgers–Korteweg–de Vries equation. Under certain conditions, the remainder is estimated with respect to the residual.

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