Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate

Shuichi Kawashima, Tohru Nakamura, Shinya Nishibata, Peicheng Zhu

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.

Original languageEnglish
Pages (from-to)2201-2235
Number of pages35
JournalMathematical Models and Methods in Applied Sciences
Volume20
Issue number12
DOIs
Publication statusPublished - Dec 1 2010

Fingerprint

Stability and Convergence
Stationary Solutions
Half-space
Convergence Rate
Sobolev spaces
Heat
Energy Method
Gases
Rate of Convergence
Asymptotic stability
Perturbation
Weighted Sobolev Spaces
Center Manifold
Large Time Behavior
Weighted Spaces
Behavior of Solutions
A Priori Estimates
Asymptotic Stability
Sobolev Spaces
Gas

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

Stationary waves to viscous heat-conductive gases in half-space : Existence, stability and convergence rate. / Kawashima, Shuichi; Nakamura, Tohru; Nishibata, Shinya; Zhu, Peicheng.

In: Mathematical Models and Methods in Applied Sciences, Vol. 20, No. 12, 01.12.2010, p. 2201-2235.

Research output: Contribution to journalArticle

Kawashima, Shuichi ; Nakamura, Tohru ; Nishibata, Shinya ; Zhu, Peicheng. / Stationary waves to viscous heat-conductive gases in half-space : Existence, stability and convergence rate. In: Mathematical Models and Methods in Applied Sciences. 2010 ; Vol. 20, No. 12. pp. 2201-2235.
@article{38350e92aa3a4af8b3447a23fa6f8644,
title = "Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate",
abstract = "The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.",
author = "Shuichi Kawashima and Tohru Nakamura and Shinya Nishibata and Peicheng Zhu",
year = "2010",
month = "12",
day = "1",
doi = "10.1142/S0218202510004908",
language = "English",
volume = "20",
pages = "2201--2235",
journal = "Mathematical Models and Methods in Applied Sciences",
issn = "0218-2025",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "12",

}

TY - JOUR

T1 - Stationary waves to viscous heat-conductive gases in half-space

T2 - Existence, stability and convergence rate

AU - Kawashima, Shuichi

AU - Nakamura, Tohru

AU - Nishibata, Shinya

AU - Zhu, Peicheng

PY - 2010/12/1

Y1 - 2010/12/1

N2 - The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.

AB - The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.

UR - http://www.scopus.com/inward/record.url?scp=78651230839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651230839&partnerID=8YFLogxK

U2 - 10.1142/S0218202510004908

DO - 10.1142/S0218202510004908

M3 - Article

AN - SCOPUS:78651230839

VL - 20

SP - 2201

EP - 2235

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 12

ER -