Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 22 (1988) no. 4, p. 535-560
@article{M2AN_1988__22_4_535_0,
     author = {Benkhaldoun, F. and Larrouturou, B.},
     title = {Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {22},
     number = {4},
     year = {1988},
     pages = {535-560},
     zbl = {0701.65097},
     mrnumber = {974288},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1988__22_4_535_0}
}
Benkhaldoun, F.; Larrouturou, B. Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 22 (1988) no. 4, pp. 535-560. http://www.numdam.org/item/M2AN_1988__22_4_535_0/

[1] G. I. Barenblatt, Y. B. Zeldovich & A. G. Istratov, Prik. Mekh. Tekh. Fiz., 2, p. 21 (1962).

[2] F. Benkhaldoun & B. Larrouturou, Explicit adaptive calculations of wrinkled flame propagation, Int. J. Num. Meth. Fluids., Vol. 7, pp. 1147-1158 (1987). | Zbl 0645.76075

[3] F. Benkhaldoun & B. Larrouturou, A finite-element adaptive investigation of two-dimensional flame front instabilities, to appear.

[4] H. Brezis, Équations d'évolution non linéaires, to appear.

[5] J. D. Buckmaster & G. S. S. Ludford, Theory of laminar flames, Cambridge University Press (1982). | MR 666866 | Zbl 0557.76001

[6] P. G. Ciarlet & P. A. Raviart, Maximum principle and uniform convergence for the finite-element method, Comp. Meth. Appl. Mech. Eng., 2, pp. 17-31 (1973). | MR 375802 | Zbl 0251.65069

[7] H. Guillard, B. Larrouturou & N. Maman, Numerical investigation of two-dimensional flame front instabilities using pseudo-spectral methods, to appear.

[8] B. Larrouturou, The equations of one-dimensional unsteady flame propagation, existence and uniqueness, SIAM J. Math. Anal., Vol. 19, N° 1, pp. 32-59 (1988). | MR 924543 | Zbl 0662.35090

[9] A. Pazy, Semigroups oflinear operators and applications to partial differential equations, Springer Verlag, New York (1983). | MR 710486 | Zbl 0516.47023

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

[11] G. Stamfacchia, Equations elliptiques du second ordre à coefficients discontinus, Presses Univ. Montréal, Montréal (1966). | MR 251373 | Zbl 0151.15501

[12] F. A. Williams, Combustion theory (second édition), Benjamin Cummings, Menlo Park (1985).