Formules min-max pour les vitesses d'ondes progressives multidimensionnelles
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 8 (1999) no. 2, pp. 259-280.
@article{AFST_1999_6_8_2_259_0,
     author = {Hamel, Fran\c{c}ois},
     title = {Formules min-max pour les vitesses d'ondes progressives multidimensionnelles},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {259--280},
     publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences},
     address = {Toulouse},
     volume = {6e s{\'e}rie, 8},
     number = {2},
     year = {1999},
     mrnumber = {1751443},
     zbl = {0956.35041},
     language = {fr},
     url = {http://www.numdam.org/item/AFST_1999_6_8_2_259_0/}
}
TY  - JOUR
AU  - Hamel, François
TI  - Formules min-max pour les vitesses d'ondes progressives multidimensionnelles
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 1999
SP  - 259
EP  - 280
VL  - 8
IS  - 2
PB  - Université Paul Sabatier. Faculté des sciences
PP  - Toulouse
UR  - http://www.numdam.org/item/AFST_1999_6_8_2_259_0/
LA  - fr
ID  - AFST_1999_6_8_2_259_0
ER  - 
%0 Journal Article
%A Hamel, François
%T Formules min-max pour les vitesses d'ondes progressives multidimensionnelles
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1999
%P 259-280
%V 8
%N 2
%I Université Paul Sabatier. Faculté des sciences
%C Toulouse
%U http://www.numdam.org/item/AFST_1999_6_8_2_259_0/
%G fr
%F AFST_1999_6_8_2_259_0
Hamel, François. Formules min-max pour les vitesses d'ondes progressives multidimensionnelles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 8 (1999) no. 2, pp. 259-280. http://www.numdam.org/item/AFST_1999_6_8_2_259_0/

[1] Agmon (S.), Nirenberg (L.). - Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math. 16 (1963), pp 121-239. | MR | Zbl

[2] Aronson (D.G.), Weinberger (H.F.). - Nonlinear diffusion in population genetics, combustion and nerve propagation, In: Part. Diff. Eq. and Related Topics, Lectures Notes in Math. 446, Springer, New York, 1975, pp 5-49. | MR | Zbl

[3] Berestycki (H.), Caffarelli (L.), Nirenberg (L.). - Uniform estimates for regularisation of free boundary problems, In: Anal. and Part. Diff. Eq., C. Sadosky & M. Decker Eds., 1990, pp 567-617. | Zbl

[4] Berestycki (H.), Hamel (F.). - Non-existence of travelling fronts solutions for some bistable reaction-diffusion equations, Adv. Diff. Equations, à paraître. | MR | Zbl

[5] Berestycki (H.), Larrouturou (B.). - A semilinear elliptic equation in a strip arising in a two-dimensional flame propagation model, J. Reine Angew. Math. 396 (1989), pp 14-40. | MR | Zbl

[6] Berestycki (H.), Larrouturou (B.), Lions (P.L.). - Multidimensional travelling-wave solutions of a flame propagation model, Arch. Rat. Mech. Anal. 111 (1990), pp 33-49. | MR | Zbl

[7] Berestycki (H.), Nicolaenko (B.), Scheurer (B.). - Traveling waves solutions to combustion models and their singular limits, SIAM J. Math. Anal. 16 (1985), pp 1207-1242. | MR | Zbl

[8] Berestycki (H.), Nirenberg (L.). - On the method of moving planes and the sliding method, Bol. da Soc. Brasileira de Matematica 22 (1991), pp 1-37. | MR | Zbl

[9] Berestycki (H.), Nirenberg (L.). - Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin. 9 (1992), pp 497-572. | Numdam | MR | Zbl

[10] Berestycki (H.), L. Nirenberg (L.), Varadhan (S.R.S.). - The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994), pp 47-92. | MR | Zbl

[11] Bramson (M.). - Convergence of solutions of the Kolmogorov equation to travelling waves, Memoirs Amer. Math. Soc. 44, 1983. | MR | Zbl

[12] Clavin (P.). - Premixed combustion and gasdynamics, Ann. Rev. Fluid Mech. 26 (1994), pp 321-352. | MR | Zbl

[13] Clavin (P.), Williams (F.A.). - Theory of premixed flame propagation in largescale turbulence, J. Fluid. Mech. 90 (1979), pp 589-604. | Zbl

[14] Donsker (M.), Varadhan (S.R.S.). - On a variational formula for the principle eigenvalue for operators with maximum principle, Proc. Nat. Acad. Sci. USA 72 (1975), pp 780-783. | MR | Zbl

[15] Fife (P.C.). - Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics 28, Springer Verlag, 1979. | MR | Zbl

[16] Fife (P.C.), Mcleod (J.B.). - The approach of solutions of non-linear diffusion equations to travelling front solutions, Arch. Rat. Mech. Anal. 65 (1977), pp 335-361. | MR | Zbl

[17] Fisher (R.A.). - The advance of advantageous genes, Ann. Eugenics 7 (1937), pp 335-369. | JFM | MR

[18] Freidlin (M.). - Wave front propagation for KPP type equations, In: Surveys in Appl. Math. 2, Plenum, New York, 1995, pp 1-62. | MR | Zbl

[19] Hadeler (K.P.), Rothe (F.). - Travelling fronts in nonlinear diffusion equations, J. Math. Biology 2 (1975), pp 251-263. | MR | Zbl

[20] Hamel (F.). - Reaction-diffusion problems in cylinders with no invariance by translation, Part II : Monotone perturbations, Ann. Inst. H. Poincaré, Anal. Non Lin. 14 (1997), pp 555-596. | Numdam | MR | Zbl

[21] Kanel' (Ya.I.). - Certain problems of burning-theory equations, Sov. Math. Dok. 2 (1961), pp 48-51. | MR | Zbl

[22] Kan-On (Y.). - Parameter dependance of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal. 26 (1995), pp 340-363. | MR | Zbl

[23] Kolmogorov (A.N.), Petrovsky (I.G.), Piskunov (N.S.). - Etude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Univ. d'Etat Moscou, Série internationale A 1 (1937), pp 1-26.

[24] Mischaikow (K.), Hutson (V.), Travelling waves for mutualist species, SIAM J. Math. Anal. 24 (1993), pp 987-1008. | MR | Zbl

[25] N. Peters (N.), Williams (F.A.). - The asymptotic structure of stoichiometric methane-air flames, Comb. Flame 68 (1987), pp 185-207.

[26] Roquejoffre (J.-M.). - Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin. 14 (1997), pp 499-552. | Numdam | MR | Zbl

[27] Rosen (G.). - Generalization of the laminar flame action principle for Arrheniustype rate functions, J. Chem. Phys. 32 (1960), pp 311-312.

[28] Stokes (A.N.). - On two types of moving front in quasilinear diffusion, Math. Biosciences 31 (1976), pp 307-315. | MR | Zbl

[29] Vega (J.-M.). - Multidimensional travelling fronts in a model from combustion theory and related problems, Diff. Int. Eq. 6 (1993), pp 131-155. | MR | Zbl

[30] Vega (J.-M.). - On the uniqueness of multidimensional travelling fronts of some semilinear equations, J. Math. Anal. Appl. 177 (1993), pp 481-490. | MR | Zbl

[31] Volpert (V.A.), Volpert (A.I.). - Determination of the asymptotic of the combustion wave velocity by successive approximations, J. App. Mech. Tech. Phys. 31 (1990), pp 680-686. | MR

[32] Volpert (A.I.), Volpert (V.A.), Volpert (V.A.). - Traveling wave solutions of parabolic systems, Translations of Math. Monographs 140, Amer. Math. Soc., 1994. | MR | Zbl

[33] Williams (F.). - Combustion Theory, Addison-Wesley, Reading MA, 1983.

[34] Xin (X.). - Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity, Idiana Univ. Math. J. 40 (1991), pp 985-1008. | MR | Zbl

[35] Xin (X.). - Existence and stability of travelling waves in periodic media governed by a bistable nonlinearity, J. Dyn. Diff. Eq. 3 (1991), pp 541-573. | MR | Zbl

[36] Zeldovich (J.B.), Frank-Kamenetskii (D.A.). - A theory of thermal propagation of flame, Acta Physiochimica URSS 9 (1938), pp 341-350. English translation: in Dynamics of curved fronts, R. Pelcé Ed., Perspectives in Physics Series, Academic Press, New York 1988, pp 131-140.