Global existence and large time asymptotic bounds of L solutions of thermal diffusive combustion systems on n
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 4, p. 625-642
@article{ASNSP_1996_4_23_4_625_0,
     author = {Collet, P. and Xin, J.},
     title = {Global existence and large time asymptotic bounds of $L^\infty $ solutions of thermal diffusive combustion systems on $\mathbb {R}^n$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 23},
     number = {4},
     year = {1996},
     pages = {625-642},
     zbl = {0882.35058},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1996_4_23_4_625_0}
}
Collet, P.; Xin, J. Global existence and large time asymptotic bounds of $L^\infty $ solutions of thermal diffusive combustion systems on $\mathbb {R}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 23 (1996) no. 4, pp. 625-642. http://www.numdam.org/item/ASNSP_1996_4_23_4_625_0/

[1] N. Alikakos, Lp bounds of solutions of the reaction-diffusion equations, Comm. Partial Differential Equations 4 (1979), 827-868. | MR 537465 | Zbl 0421.35009

[2] J.D. Avrin, Qualitative theory for a model of laminar flames with arbitrary nonnegative initial data, J. Differential Equations 84 (1990), 290-308. | MR 1047571 | Zbl 0712.35047

[3] H. Berestycki - B. Larrouturou, Quelque aspects mathématique de la propagation des flammes prémélangées, in: "Nonlinear pde and their applications", Pitman Research Notes in Math Series 220, eds. H. Brezis and J. L. Lions, Collège de France, Vol. 10, 1991. | MR 1131819 | Zbl 0755.35090

[4] L. Berlyand - J. Xin, Large time asymptotics of solutions to a model combustion system with critical nonlinearity, Nonlinearity 8 (1995), 161-178. | MR 1328592 | Zbl 0820.35081

[5] J. Billingham - D.J. Needham, The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form traveling waves, Philos. Trans. Roy. Soc. London Ser. A334 (1991), 1-24. | MR 1155096 | Zbl 0739.35033

[6] J. Billingham - D.J. Needham, The development of traveling waves in quadratic and cubic autocatalysis with unequal diffusion rates. II. An initial-value problem with an immobilized or nearly immobilized autocatalyst, Philos. Trans. Roy. Soc. London A 336 (1991), 497-539. | MR 1133118 | Zbl 0762.35048

[7] A. Bonnet - B. Larrouturou - L. Sainsaulieu, On the stability of multiple steady planar flames when the Lewis number is less than one, Phys. Rev. D 69 (1993), 345-352. | Zbl 0802.76090

[8] J. Bricmont - A. Kupiainen - J. Xin, Global large time self-similarity of a thermal diffusive combustion system with critical nonlinearity, J. Differential Equations 130 (1996), 9-35. | MR 1409021 | Zbl 0862.35050

[9] P. Clavin, Dynamical behavior of premixed flame fronts in laminar and turbulent flows, Progress in Energy and Combustion Science 11 (1975), 1169-1190.

[10] P. Collet, Thermodynamic limit of the Ginzburg-Landau equations, Nonlinearity 7 (1994), 1175-1190. | MR 1284687 | Zbl 0803.35066

[11] P. Collet - J-P. ECKMANN, The time dependent amplitude equation for the Swift-Hohenberg problem, Comm. Math. Phys. 132 (1990), 135-153. | MR 1069205 | Zbl 0756.35096

[12] A. Haraux - A. Youkana, On a Result of K. Masuda Concerning Reaction-Diffusion Equations, Tôhoku Math. J. 40 (1988), 159-163. | MR 927083 | Zbl 0689.35041

[13] S. Hollis - R. Martin - M. Pierre, Global existence and boundedness in reaction-diffusion systems, SIAM J. Math Anal. 18 (1987), 744-761. | MR 883566 | Zbl 0655.35045

[14] B. Larrouturou, The equations of one-dimensional unsteady flame propagation: existence and uniqueness, SIAM J. Math. Anal. 19 (1988), 32-59. | MR 924543 | Zbl 0662.35090

[15] O. Manley - M. Marion - R. Temam, Equations of Combustion in the Presence of Complex Chemistry, Indiana Univ. Math. J. 42 (1993), 941-965. | MR 1254127 | Zbl 0796.35164

[16] R.H. Martin - M. Pierre, Nonlinear reaction-diffusion systems, in: "Nonlinear Equations in the Applied Sciences", W.F.Ames and C. Rogers eds., Academic Press, Boston, 1992. | MR 1132045 | Zbl 0781.35030

[17] K. Masuda, On the global existence and asymptotic behavior of solutions of reaction-diffusion equations, Hokkaido Math J. 12 (1983), 360-370. | MR 719974 | Zbl 0529.35037

[18] B.J. Matkowsky - G.I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. Appl. Math. 37 (1979), 686-699. | MR 549149 | Zbl 0437.76065

[19] G.I. Sivashinsky, Instabilities, pattern formation and turbulence in flames, Ann. Rev. Fluid Mech. 15 (1983), 179-199. | Zbl 0538.76053

[20] D. Terman, Stability of planar wave solutions to a combustion model, SIAM J. Math. Anal. 21 (1990), 1139-1171. | MR 1062397 | Zbl 0723.35011