Article
MSC:
35A01,
35A02,
35L60,
35L65,
35N10,
35Q30,
76N15 | MR 2899727 | Zbl 1249.35251 | DOI: 10.1007/s10492-012-0008-9
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Keywords:
reactive and radiative gas; global solution; global a priori estimates
reactive and radiative gas; global solution; global a priori estimates
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.
References:
[1] Antontsev, S. N., Kazhikhov, A. V., Monakhov, V. N.: Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. North-Holland Amsterdam (1990). MR 1035212 | Zbl 0696.76001
[2] Bebernes, J., Bressan, A.: Global a priori estimates for a viscous reactive gas. Proc. R. Soc. Edinb., Sect. A 101 (1985), 321-333. DOI 10.1017/S0308210500020862 | MR 0824230 | Zbl 0614.76076
[3] Bebernes, J., Eberly, D.: Mathematical Problems from Combustion Theory. Springer New York (1989). MR 1012946 | Zbl 0692.35001
[4] Chen, G.-Q.: Global solution to the compressible Navier-Stokes equations for a reacting mixture. SIAM J. Math. Anal. 23 (1992), 609-634. DOI 10.1137/0523031 | MR 1158824
[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. DOI 10.1007/s00205-002-0233-6 | MR 1961444
[6] Ducomet, B.: Hydrodynamical models of gaseous stars. Rev. Math. Phys. 8 (1996), 957-1000. DOI 10.1142/S0129055X96000354 | MR 1415382 | Zbl 0949.76071
[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. DOI 10.1002/(SICI)1099-1476(199910)22:15<1323::AID-MMA80>3.0.CO;2-8 | MR 1710987 | Zbl 1027.85005
[8] Ducomet, B.: Global existence for a nuclear fluid in one dimension: the $T>0$ case. Appl. Math. 47 (2002), 45-75. DOI 10.1023/A:1021754900964 | MR 1876491 | Zbl 1090.76517
[9] Ducomet, B., Zlotnik, A.: Lyapunov functional method for 1D radiative and reactive viscous gas dynamics. Arch. Ration. Mech. Anal. 177 (2005), 185-229. DOI 10.1007/s00205-005-0363-8 | MR 2188048 | Zbl 1070.76044
[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. DOI 10.1016/j.na.2005.03.064 | MR 2211579 | Zbl 1083.35109
[11] Song, J.: On initial boundary value problems for a viscous heat-conducting one-dimensional real gas. J. Differ. Equations 110 (1994), 157-181. DOI 10.1006/jdeq.1994.1064 | MR 1278368
[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. DOI 10.1016/0022-0396(85)90023-3 | MR 0791841 | Zbl 0579.35052
[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. DOI 10.1016/0021-8928(77)90011-9 | MR 0468593
[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. DOI 10.1016/j.na.2003.12.001 | MR 2070619 | Zbl 1094.76052
[15] Mihalas, D., Mihalas, B. Weibel: Foundations of Radiation Hydrodynamics. Oxford University Press New York (1984). MR 0781346
[16] Shelukhin, V. V.: A shear flow problem for the compressible Navier-Stokes equations. Int. J. Non-Linear Mech. 33 (1998), 247-257. DOI 10.1016/S0020-7462(97)00010-3 | MR 1469854 | Zbl 0894.76071
[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. DOI 10.1146/annurev.fl.13.010181.000455 | Zbl 0492.76074
[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. DOI 10.1016/j.jde.2006.09.023 | MR 2300663 | Zbl 1119.35070
[19] Wang, D.: Global solution for the mixture of real compressible reacting flows in combustion. Commun. Pure Appl. Anal. 3 (2004), 775-790. DOI 10.3934/cpaa.2004.3.775 | MR 2106299 | Zbl 1064.76091
[20] Williams, F. A.: Combustion Theory: The Fundamental Theory of Chemically Reacting Flow System. 2nd ed. Benjamin-Cummings Publ. Co. San Francisco (1985).
[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. DOI 10.1007/BF03167320 | MR 1651737 | Zbl 0912.76077
[22] Zel'dovich, Y. B., Raizer, Y. P.: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Vol. 2. Academic Press New Work (1967).
[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. DOI 10.1023/B:MATN.0000015045.35518.a4 | MR 2054563 | Zbl 1122.35118
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