Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction
type: Item
instance of: scholarly article
title: Backward uniqueness of the s.c. semigroup arising in parabolic-hyperbolic fluid-structure interaction
zbMATH Open document ID: 1158.35300
author: G. Avalos
author: R. Triggiani
published in: Journal of Differential Equations
publication date: 2008-07-11T00:00:00Z
review text: The asymptotic behavior of a spherically symmetric flow of a compressible viscous and polytropic ideal fluid in a field of external forces over an unbounded exterior domain of a sphere in \(n\)-dimensional space are considered. The unique existence of the stationary solution is shown under the adhesion and the adiabatic boundary conditions. Then, it is shown that a solution to the initial boundary value problem with the same boundary and spatial asymptotic conditions uniquely exists globally in time and converges to the stationary solution as time tends to infinity. In this stability theorem, the initial data can be chosen arbitrarily large as far as it belongs to suitable Sobolev space. Moreover, if the external force is attractive to the center of the sphere, it can be taken arbitrarily large. The proof of the stability theorem is based on the standard energy method using the Lagrangian coordinates. Here, it is the essential step to obtain the pointwise estimate of the density and the absolute temperature uniformly in time. The former is obtained through estimating the representation formula of density with the aid of the energy estimate.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 74F10
Mathematics Subject Classification ID: 76N15
zbMATH DE Number: 5300793
zbMATH Keywords: heat-conductive gas
zbMATH Keywords: potential forces
zbMATH Keywords: spherically symmetric flow
zbMATH Keywords: unbounded exterior domain
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: energy method
zbMATH Keywords: Lagrangian coordinates
MaRDI profile type: Publication
full work available at URL: j.jde.2007.10.036
OpenAlex ID: W2057860370
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DOI: 10.1016/J.JDE.2007.10.036
description: scientific article; zbMATH DE number 5300793