The asymptotic behavior of the moments of solutions to the non-Hermitian linear system of equations of high-performance column chromatography (Q403889): Difference between revisions

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.