Computational aspects of finding a solution asymptotics for a singularly perturbed system of differential equations

TL;DR

This paper investigates the asymptotic behavior of solutions to singularly perturbed mass transfer systems, linking degeneracy in the leading term to system parameters, with implications for computational methods.

Contribution

It establishes a theorem connecting degeneracy degree with system size and variables, and proposes a hypothesis for general cases, reducing reliance on eigenvalue calculations.

Findings

Relationship between degeneracy and system parameters

Theorem linking asymptotics to system structure

Hypothesis on general case existence

Abstract

We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We prove a theorem that establishes a relationship between the degree of degeneracy and the numbers of equations in the system and spatial variables in some particular cases. The work hardly depends on the calculation of the eigenvalues of matrices that determine the spatial structure of the asymptotics by the means of computer algebra system Wolfram Mathematica. We put forward a hypothesis on the existence of the found connection for an arbitrary number of equations and spatial variables.