Large-Time Behavior of Solutions to Hyperbolic-Elliptic Coupled Systems

Shuichi Kawashima, Yoshiko Nikkuni, Shinya Nishibata

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We are concerned with the asymptotic behavior of a solution to the initial value problem for a system of hyperbolic conservation laws coupled with elliptic equations. This kind of problem was first considered in our previous paper. In the present paper, we generalize the previous results to a broad class of hyperbolic-elliptic coupled systems. Assuming the existence of the entropy function and the stability condition, we prove the global existence and the asymptotic decay of the solution for small initial data in a suitable Sobolev space. Then, it is shown that the solution is well approximated, for large time, by a solution to the corresponding hyperbolic-parabolic coupled system. The first result is proved by deriving a priori estimates through the standard energy method. The spectral analysis with the aid of the a priori estimate gives the second result.

Original languageEnglish
Pages (from-to)297-329
Number of pages33
JournalArchive for Rational Mechanics and Analysis
Volume170
Issue number4
DOIs
Publication statusPublished - 2003 Dec 1
Externally publishedYes

Fingerprint

Large Time Behavior
Elliptic Systems
Behavior of Solutions
Coupled System
A Priori Estimates
Sobolev spaces
Initial value problems
Spectrum analysis
Conservation
Hyperbolic Systems of Conservation Laws
Entropy Function
Entropy
Parabolic Systems
Energy Method
Spectral Analysis
Stability Condition
Elliptic Equations
Global Existence
Sobolev Spaces
Initial Value Problem

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Large-Time Behavior of Solutions to Hyperbolic-Elliptic Coupled Systems. / Kawashima, Shuichi; Nikkuni, Yoshiko; Nishibata, Shinya.

In: Archive for Rational Mechanics and Analysis, Vol. 170, No. 4, 01.12.2003, p. 297-329.

Research output: Contribution to journalArticle

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