On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary
type: Item
instance of: scholarly article
title: On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary
zbMATH Open document ID: 0598.34021
DOI: 10.1016/0022-0396(86)90041-0
author: Takeyuki Nagasawa
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: Several initial-boundary value problems of equations describing the one- dimensional motion of the ideal polytropic gas are discussed. In our problems the gas is put into the region where the ends are not fixed, so the (specific) volume of the gas may grow infinitely as time increases. In the article the above conjecture is shown, that is, the temporally global existence of the unique and classical solutions and the growth of the (specific) volume of the gas under some assumptions are proved. To be precise, at least under the assumption guaranteeing the global existence of the solution, the upper limit of the volume of the gas tends to infinity as time increases. Moreover, adding some (not so strong) assumptions, the (specific) volume tends to infinity, and we can find the upper and lower bounds of the order of growth.
Mathematics Subject Classification ID: 34B99
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 3964413
zbMATH Keywords: one-dimensional motion of the ideal polytropic gas
zbMATH Keywords: global existence
zbMATH Keywords: order of growth
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90041-0
OpenAlex ID: W1996654272
cites work: The effect of boundary damping for the quasilinear wave equation
cites work: On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluid
cites work: Global solutions to the initial value problem for the equations of one- dimensional motion of viscous polytropic gases
cites work: Q4126790
cites work: Le problème de Cauchy pour les équations différentielles d'un fluide général
cites work: On the first initial-boundary value problem of compressible viscous fluid motion
description: scientific article; zbMATH DE number 3964413