| Title:
|
Global existence of solutions for the 1-D radiative and reactive viscous gas dynamics (English) |
| Author:
|
Zhang, Wen |
| Author:
|
Zhang, Jianwen |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
109-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed. (English) |
| Keyword:
|
reactive and radiative gas |
| Keyword:
|
global solution |
| Keyword:
|
global a priori estimates |
| MSC:
|
35A01 |
| MSC:
|
35A02 |
| MSC:
|
35L60 |
| MSC:
|
35L65 |
| MSC:
|
35N10 |
| MSC:
|
35Q30 |
| MSC:
|
76N15 |
| idZBL:
|
Zbl 1249.35251 |
| idMR:
|
MR2899727 |
| DOI:
|
10.1007/s10492-012-0008-9 |
| . |
| Date available:
|
2012-03-05T07:01:04Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142031 |
| . |
| Reference:
|
[1] Antontsev, S. N., Kazhikhov, A. V., Monakhov, V. N.: Boundary Value Problems in Mechanics of Nonhomogeneous Fluids.North-Holland Amsterdam (1990). Zbl 0696.76001, MR 1035212 |
| Reference:
|
[2] Bebernes, J., Bressan, A.: Global a priori estimates for a viscous reactive gas.Proc. R. Soc. Edinb., Sect. A 101 (1985), 321-333. Zbl 0614.76076, MR 0824230, 10.1017/S0308210500020862 |
| Reference:
|
[3] Bebernes, J., Eberly, D.: Mathematical Problems from Combustion Theory.Springer New York (1989). Zbl 0692.35001, MR 1012946 |
| Reference:
|
[4] Chen, G.-Q.: Global solution to the compressible Navier-Stokes equations for a reacting mixture.SIAM J. Math. Anal. 23 (1992), 609-634. MR 1158824, 10.1137/0523031 |
| Reference:
|
[5] Chen, G.-Q., Hoff, D., Trivisa, K.: Global solution to a model for exothermically reacting compressible flows with large discontinuous data.Arch. Ration. Mech. Anal. 166 (2003), 321-358. MR 1961444, 10.1007/s00205-002-0233-6 |
| Reference:
|
[6] Ducomet, B.: Hydrodynamical models of gaseous stars.Rev. Math. Phys. 8 (1996), 957-1000. Zbl 0949.76071, MR 1415382, 10.1142/S0129055X96000354 |
| Reference:
|
[7] Ducomet, B.: A model of thermal dissipation for a one-dimensional viscous reactive and radiative gas.Math. Methods Appl. Sci. 22 (1999), 1323-1349. Zbl 1027.85005, MR 1710987, 10.1002/(SICI)1099-1476(199910)22:15<1323::AID-MMA80>3.0.CO;2-8 |
| Reference:
|
[8] Ducomet, B.: Global existence for a nuclear fluid in one dimension: the $T>0$ case.Appl. Math. 47 (2002), 45-75. Zbl 1090.76517, MR 1876491, 10.1023/A:1021754900964 |
| Reference:
|
[9] Ducomet, B., Zlotnik, A.: Lyapunov functional method for 1D radiative and reactive viscous gas dynamics.Arch. Ration. Mech. Anal. 177 (2005), 185-229. Zbl 1070.76044, MR 2188048, 10.1007/s00205-005-0363-8 |
| Reference:
|
[10] Ducomet, B., Zlotnik, A.: On the large-time behavior of 1D radiative and reactive viscous flows for higher-order kinetics.Nonlinear Anal., Theory Methods Appl. 63 (2005), 1011-1033. Zbl 1083.35109, MR 2211579, 10.1016/j.na.2005.03.064 |
| Reference:
|
[11] Song, J.: On initial boundary value problems for a viscous heat-conducting one-dimensional real gas.J. Differ. Equations 110 (1994), 157-181. MR 1278368, 10.1006/jdeq.1994.1064 |
| Reference:
|
[12] Kawohl, B.: Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas.J. Differ. Equations 58 (1985), 76-103. Zbl 0579.35052, MR 0791841, 10.1016/0022-0396(85)90023-3 |
| Reference:
|
[13] Kazhikhov, A. V., Shelukhin, V. V.: Unique global solution with respect to time of the initial-boundary value problems for one-dimensional equations of a viscous gas.J. Appl. Math. Mech. 41 (1977), 282-291. MR 0468593, 10.1016/0021-8928(77)90011-9 |
| Reference:
|
[14] Lewicka, M., Mucha, P. B.: On temporal asymptotics for the $p$th power viscous reactive gas.Nonlinear Anal., Theory Methods Appl. 57 (2004), 951-969. Zbl 1094.76052, MR 2070619, 10.1016/j.na.2003.12.001 |
| Reference:
|
[15] Mihalas, D., Mihalas, B. Weibel: Foundations of Radiation Hydrodynamics.Oxford University Press New York (1984). MR 0781346 |
| Reference:
|
[16] Shelukhin, V. V.: A shear flow problem for the compressible Navier-Stokes equations.Int. J. Non-Linear Mech. 33 (1998), 247-257. Zbl 0894.76071, MR 1469854, 10.1016/S0020-7462(97)00010-3 |
| Reference:
|
[17] Solonnikov, V. A., Kazhikhov, A. V.: Existence theorems for the equations of motion of a compressible viscous fluid.Ann. Rev. Fluid Mech. 13 (1981), 79-95. Zbl 0492.76074, 10.1146/annurev.fl.13.010181.000455 |
| Reference:
|
[18] Umehara, M., Tani, A.: Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas.J. Differ. Equations 234 (2007), 439-463. Zbl 1119.35070, MR 2300663, 10.1016/j.jde.2006.09.023 |
| Reference:
|
[19] Wang, D.: Global solution for the mixture of real compressible reacting flows in combustion.Commun. Pure Appl. Anal. 3 (2004), 775-790. Zbl 1064.76091, MR 2106299, 10.3934/cpaa.2004.3.775 |
| Reference:
|
[20] Williams, F. A.: Combustion Theory: The Fundamental Theory of Chemically Reacting Flow System. 2nd ed.Benjamin-Cummings Publ. Co. San Francisco (1985). |
| Reference:
|
[21] Yanagi, S.: Asymptotic stability of the solutions to a full one-dimensional system of heat-conductive, reactive, compressible viscous gas.Japan J. Ind. Appl. Math. 15 (1998), 423-442. Zbl 0912.76077, MR 1651737, 10.1007/BF03167320 |
| Reference:
|
[22] Zel'dovich, Y. B., Raizer, Y. P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Vol. 2.Academic Press New Work (1967). |
| Reference:
|
[23] Zlotnik, A.: Weak solutions to the equations of motion of viscous compressible reacting binary mixtures: uniqueness and Lipschitz-continuous dependence on data.Math. Notes 75 (2004), 307-311. Zbl 1122.35118, MR 2054563, 10.1023/B:MATN.0000015045.35518.a4 |
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