### 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 language | English |
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Pages (from-to) | 567-589 |

Number of pages | 23 |

Journal | Indiana University Mathematics Journal |

Volume | 50 |

Issue number | 1 |

Publication status | Published - 2001 Mar 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Indiana University Mathematics Journal*,

*50*(1), 567-589.

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

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 50, no. 1, pp. 567-589.

}

TY - JOUR

T1 - A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics

AU - Kawashima, Shuichi

AU - Nishibata, Shinya

PY - 2001/3/1

Y1 - 2001/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039296495&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039296495&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039296495

VL - 50

SP - 567

EP - 589

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 1

ER -