Abstract

The Cauchy problem for a singularly perturbed system of equations describing a transport process with diffusion in a multiphase medium is considered. A formal asymptotic expansion of its solution is constructed in the case when exchange between the phases proceeds much more rapidly than the transport and diffusion processes. The case when the diffusion fluxes of the components have a mutual effect on each other is considered. Under the assumptions imposed on the data of the problem, the leading term of the asymptotics is described by a multidimensional generalized Burgers–Korteweg–de Vries equation. Under some additional conditions, the remainder is estimated by means of the residual.

中文翻译：

---

弱相互扩散对多相介质中输运过程的影响

摘要

考虑了奇异摄动方程组的柯西问题，该方程描述了在多相介质中具有扩散的传输过程。当相之间的交换比传输和扩散过程快得多时，构造其解的形式渐近展开。考虑了组分的扩散通量相互影响的情况。在对问题数据施加假设的前提下，渐近项的首项由多维广义Burgers–Korteweg–de Vries方程描述。在某些附加条件下，余数通过残差估算。