A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics

Shuichi Kawashima, Shinya Nishibata

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We discuss the singular limit of solutions to the initial value problem for a certain class of hyperbolic-elliptic coupled systems. A typical example of this problem appears in radiation hydrodynamics. It is shown that the singular limit problem of the hyperbolic-elliptic system corresponds to the concrete physical problem of making the Boltzmann number become infinitesimal and the Bouguer number become infinite, with their product kept constant. We show that the solution to the hyperbolic-elliptic coupled system converges to the solution of the corresponding hyperbolic-parabolic coupled system. First, the global existence is proved by the uniform estimate which is obtained through the standard energy method. Then applying the uniform estimate, we prove the convergence of the solution.

Original languageEnglish
Pages (from-to)567-589
Number of pages23
JournalIndiana University Mathematics Journal
Volume50
Issue number1
Publication statusPublished - 2001 Mar 1
Externally publishedYes

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Singular Limit
Elliptic Systems
Coupled System
Hydrodynamics
Uniform Estimates
Radiation
Parabolic Systems
Energy Method
Hyperbolic Systems
Ludwig Boltzmann
Global Existence
Initial Value Problem
Converge

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics. / Kawashima, Shuichi; Nishibata, Shinya.

In: Indiana University Mathematics Journal, Vol. 50, No. 1, 01.03.2001, p. 567-589.

Research output: Contribution to journalArticle

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