The asymptotic behavior of the moments of solutions to the non-Hermitian linear system of equations of high-performance column chromatography
type: Item
instance of: scholarly article
title: The asymptotic behavior of the moments of solutions to the non-Hermitian linear system of equations of high-performance column chromatography
zbMATH Open document ID: 1302.35378
DOI: 10.1134/S1064562413060203
author: A. G. Prudkovskii
published in: Doklady Mathematics
publication date: 2014-08-29T00:00:00Z
review text: The author has considered the Cauchy problem for the generalized system of equations of high-performance chromatography with non-Hermitian matrix in the most general statement, to which the estimation methods used in [\textit{V. P. Maslov}, Operator methods (Russian). Moscow: Nauka (1973; Zbl 0288.47042)] are not applicable. The system of the form \[ h\frac{\partial z_i}{\partial t}=\sum\limits_{j}A_{ij}z_j -h\delta_i\frac{\partial }{\partial x}(vz_i)+h^2\frac{\partial }{\partial x}(D_i\frac{\partial z}{\partial x}),\; \bar{z}(x,o)=z_0(x),\; i,j=\bar{1,n} \] where \(z_i(x,t)\) are the probability densities of the occurrence of the component substance in the moving on stationary phase correspondingly when \(\delta_i\) is equal to unit or zero. The problem is solved in the 2-dimensional space \((x\in (-\infty, \infty), t\in [o,T]).\) The aim of the article is to describe the asymptotic behavior of the first two moments of the solution, necessary for chromatography.
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6336239
zbMATH Keywords: parabolic system of equations
zbMATH Keywords: two-dimensional space
zbMATH Keywords: Cauchy problem with respect to probability density
zbMATH Keywords: asymptotic behavior of first two moments of solution
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Q4776464
cites work: The method of moments as applied to a system of high-performance column chromatography
full work available at URL: s1064562413060203
OpenAlex ID: W2071144720
description: scientific article; zbMATH DE number 6336239