Mathematical model of pollution and self-purification of the environment
type: Item
instance of: scholarly article
zbMATH Open document ID: 0957.35070
author: M. A. Berezovs'kyj
author: S. M. Doguchayeva
publication date: 2001-03-01T00:00:00Z
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 1571615
zbMATH Keywords: pollution of environment
zbMATH Keywords: non-local problem
zbMATH Keywords: explicit solution
zbMATH Keywords: approximate solution
MaRDI profile type: Publication
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title: Mathematical model of pollution and self-purification of the environment
published in: Visnyk. Seriya: Fizyko-Matematychni Nauky. Kyïvs'kyĭ Universytet Imeni Tarasa Shevchenka
review text: The authors investigate the following mathematical model of pollution of the environment with turbulent diffusion, adsorption and disintegration of active admixtures NEWLINE\[NEWLINE {\partial^{2}u\over\partial x^{2}}- {\partial u\over\partial t}=x^{1-\beta}u^{\beta},\quad 0<x<s(t),\quad t>0, \quad u(x,0)=0,\quad 0<x<s(0), NEWLINE\]NEWLINE NEWLINE\[NEWLINE u(s(t),t)=u_{x}(s(t),t)=0,\quad t>0,\quad \int\limits_{0}^{s(t)}\left(u_{t}+x^{1-\beta}u^{\beta}\right)x dx= q(t),\quad t>0. NEWLINE\]NEWLINE In the cases \(\beta=0,1\) exact solutions of the corresponding stationary problems are obtained. For the non-stationary problems a constructive method for the approximate solution is proposed.
reviewed by: Aleksandr D. Borisenko
description: scientific article