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 |
|---|---|
| Pages (from-to) | 567-589 |
| Number of pages | 23 |
| Journal | Indiana University Mathematics Journal |
| Volume | 50 |
| Issue number | 1 |
| Publication status | Published - Mar 1 2001 |
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All Science Journal Classification (ASJC) codes
- 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 journal › Article
}
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.
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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 -