The asymptotic behavior of the moments of solutions to the non-Hermitian linear system of equations of high-performance column chromatography
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.
Cauchy problem with respect to probability density
asymptotic behavior of first two moments of solution
scientific article; zbMATH DE number 6336239