On the initial-boundary value problems for barotropic motions of a viscous gas in a region with permeable boundaries
type: Item
instance of: scholarly article
title: On the initial-boundary value problems for barotropic motions of a viscous gas in a region with permeable boundaries
zbMATH Open document ID: 0812.35096
author: S. Ya. Belov
published in: Journal of Mathematics of Kyoto University
publication date: 1994-12-19T00:00:00Z
review text: For the pair of functions \(u(g,t)\), \(\rho(y,t)\) the following system of equations is considered in a rectangle \(Q= \{(y,t)\): \(0<y<Y\), \(0<t<T\}\) \[ \rho \biggl( {{\partial u} \over {\partial t}}+u {{\partial u} \over {\partial y}} \biggr)=\mu {{\partial^ 2 u} \over {\partial y^ 2}}- {\partial \over {\partial y}} (\rho^ \gamma), \qquad {{\partial\rho} \over {\partial t}}+u {{\partial\rho} \over {\partial y}}+\rho {{\partial u} \over {\partial y}} =0 \tag{1} \] under the initial conditions \[ u(y,0) = u_ 0(y), \qquad \rho(y,0)= \rho_ 0(y), \qquad 0\leq y\leq Y,\tag{2} \] and one of the boundary conditions stated below \[ \begin{aligned} u(0,t) &= u_ 1(t)>0, \qquad \rho(0,t)= \rho_ 1(t), \qquad u(Y,t)= u_ 2(t)\geq 0, \tag{3}\\ u(0,t) &= u_ 1(t)>0, \qquad \rho(0,t)= \rho_ 1(t), \qquad \rho(Y,t)= \rho_ 2(t), \tag{4}\\ u(0,t) &= u_ 1(t)<0, \qquad u(Y,t)= u_ 2(t)\geq 0. \tag{5} \end{aligned} \] The solvability of the problems (1), (2), (3); (1), (2), (4) and (1) (2), (5) are proved in Sobolev and in Hölder spaces.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 701492
zbMATH Keywords: viscous gas
zbMATH Keywords: permeable boundaries
zbMATH Keywords: one-dimensional motion
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519016
OpenAlex ID: W1508368045
DOI: 10.1215/KJM/1250519016
Recommended article: Q4734971
Recommended article: Q4734972
Recommended article: Q3313501
Recommended article: On bounds for solutions to finite-difference equations for one- dimensional flow of viscous barotropic gas
Recommended article: Q4352069
Recommended article: Q3364056
Recommended article: The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spaces \(W_ 2^{2+\ell,1+\ell/2}(Q_ T)\)
Recommended article: Q5184568
Recommended article: Q5184569
Recommended article: Global properties of a difference approximation of the free boundary problem for symmetric motion of a viscous barotropic gas
description: scientific article; zbMATH DE number 701492