Global existence and large time asymptotic bounds of $L^{\infty }$ solutions of thermal diffusive combustion systems on ${ℝ}^n$

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1. [1] N. Alikakos, Lp bounds of solutions of the reaction-diffusion equations, Comm. Partial Differential Equations4 (1979), 827-868. Zbl0421.35009MR537465
2. [2] J.D. Avrin, Qualitative theory for a model of laminar flames with arbitrary nonnegative initial data, J. Differential Equations84 (1990), 290-308. Zbl0712.35047MR1047571
3. [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. Zbl0755.35090MR1131819
4. [4] L. Berlyand - J. Xin, Large time asymptotics of solutions to a model combustion system with critical nonlinearity, Nonlinearity8 (1995), 161-178. Zbl0820.35081MR1328592
5. [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. Zbl0739.35033MR1155096
6. [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. LondonA336 (1991), 497-539. Zbl0762.35048MR1133118
7. [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. D69 (1993), 345-352. Zbl0802.76090
8. [8] J. Bricmont - A. Kupiainen - J. Xin, Global large time self-similarity of a thermal diffusive combustion system with critical nonlinearity, J. Differential Equations130 (1996), 9-35. Zbl0862.35050MR1409021
9. [9] P. Clavin, Dynamical behavior of premixed flame fronts in laminar and turbulent flows, Progress in Energy and Combustion Science11 (1975), 1169-1190. 
10. [10] P. Collet, Thermodynamic limit of the Ginzburg-Landau equations, Nonlinearity7 (1994), 1175-1190. Zbl0803.35066MR1284687
11. [11] P. Collet - J-P. ECKMANN, The time dependent amplitude equation for the Swift-Hohenberg problem, Comm. Math. Phys.132 (1990), 135-153. Zbl0756.35096MR1069205
12. [12] A. Haraux - A. Youkana, On a Result of K. Masuda Concerning Reaction-Diffusion Equations, Tôhoku Math. J.40 (1988), 159-163. Zbl0689.35041MR927083
13. [13] S. Hollis - R. Martin - M. Pierre, Global existence and boundedness in reaction-diffusion systems, SIAM J. Math Anal.18 (1987), 744-761. Zbl0655.35045MR883566
14. [14] B. Larrouturou, The equations of one-dimensional unsteady flame propagation: existence and uniqueness, SIAM J. Math. Anal.19 (1988), 32-59. Zbl0662.35090MR924543
15. [15] O. Manley - M. Marion - R. Temam, Equations of Combustion in the Presence of Complex Chemistry, Indiana Univ. Math. J.42 (1993), 941-965. Zbl0796.35164MR1254127
16. [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. Zbl0781.35030MR1132045
17. [17] K. Masuda, On the global existence and asymptotic behavior of solutions of reaction-diffusion equations, Hokkaido Math J.12 (1983), 360-370. Zbl0529.35037MR719974
18. [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. Zbl0437.76065MR549149
19. [19] G.I. Sivashinsky, Instabilities, pattern formation and turbulence in flames, Ann. Rev. Fluid Mech.15 (1983), 179-199. Zbl0538.76053
20. [20] D. Terman, Stability of planar wave solutions to a combustion model, SIAM J. Math. Anal.21 (1990), 1139-1171. Zbl0723.35011MR1062397