Formules min-max pour les vitesses d'ondes progressives multidimensionnelles
Annales de la Faculté des sciences de Toulouse : Mathématiques (1999)
- Volume: 8, Issue: 2, page 259-280
- ISSN: 0240-2963
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topHamel, François. "Formules min-max pour les vitesses d'ondes progressives multidimensionnelles." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.2 (1999): 259-280. <http://eudml.org/doc/73487>.
@article{Hamel1999,
author = {Hamel, François},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {travelling-wave solutions; reaction-diffusion equations; min-max formula},
language = {fre},
number = {2},
pages = {259-280},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Formules min-max pour les vitesses d'ondes progressives multidimensionnelles},
url = {http://eudml.org/doc/73487},
volume = {8},
year = {1999},
}
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
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 2
SP - 259
EP - 280
LA - fre
KW - travelling-wave solutions; reaction-diffusion equations; min-max formula
UR - http://eudml.org/doc/73487
ER -
References
top- [1] Agmon ( S.), Nirenberg ( L.). - Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math.16 (1963), pp 121-239. Zbl0117.10001MR155203
- [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. Zbl0325.35050MR427837
- [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. Zbl0702.35252
- [4] Berestycki ( H.), Hamel ( F.). — Non-existence of travelling fronts solutions for some bistable reaction-diffusion equations, Adv. Diff. Equations, à paraître. Zbl0988.35081MR1750116
- [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. Zbl0658.35036MR988546
- [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. Zbl0711.35066MR1051478
- [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. Zbl0596.76096MR807905
- [8] Berestycki ( H.), Nirenberg ( L.). - On the method of moving planes and the sliding method, Bol. da Soc. Brasileira de Matematica22 (1991), pp 1-37. Zbl0784.35025MR1159383
- [9] Berestycki ( H.), Nirenberg ( L.). - Travelling fronts in cylinders, Ann. Inst. H. Poincaré, Anal. Non Lin.9 (1992), pp 497-572. Zbl0799.35073MR1191008
- [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. Zbl0806.35129MR1258192
- [11] Bramson ( M.). — Convergence of solutions of the Kolmogorov equation to travelling waves, Memoirs Amer. Math. Soc.44, 1983. Zbl0517.60083MR705746
- [12] Clavin ( P.). - Premixed combustion and gasdynamics, Ann. Rev. Fluid Mech.26 (1994), pp 321-352. Zbl0802.76070MR1262140
- [13] Clavin ( P.), Williams ( F.A.). - Theory of premixed flame propagation in largescale turbulence, J. Fluid. Mech.90 (1979), pp 589-604. Zbl0434.76052
- [14] Donsker ( M.), Varadhan ( S.R.S.). — On a variational formula for the principle eigenvalue for operators with maximum principle, Proc. Nat. Acad. Sci. USA72 (1975), pp 780-783. Zbl0353.49039MR361998
- [15] Fife ( P.C.). — Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics28, Springer Verlag, 1979. Zbl0403.92004MR527914
- [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. Zbl0361.35035MR442480
- [17] Fisher ( R.A.). - The advance of advantageous genes, Ann. Eugenics7 (1937), pp 335-369. MR2079JFM63.1111.04
- [18] Freidlin ( M.). — Wave front propagation for KPP type equations, In: Surveys in Appl. Math.2, Plenum, New York, 1995, pp 1-62. Zbl0848.60065MR1387615
- [19] Hadeler ( K.P.), Rothe ( F.). - Travelling fronts in nonlinear diffusion equations, J. Math. Biology2 (1975), pp 251-263. Zbl0343.92009MR411693
- [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. Zbl0902.35036MR1470782
- [21] KANEL' ( Ya.I.). — Certain problems of burning-theory equations, Sov. Math. Dok.2 (1961), pp 48-51. Zbl0138.35103MR117429
- [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. Zbl0821.34048MR1320224
- [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 A1 (1937), pp 1-26. Zbl0018.32106
- [24] Mischaikow ( K.), Hutson ( V.), Travelling waves for mutualist species, SIAM J. Math. Anal.24 (1993), pp 987-1008. Zbl0815.35044MR1226860
- [25] N. PETERS ( N.), Williams ( F.A.). — The asymptotic structure of stoichiometric methane-air flames, Comb. Flame68 (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. Zbl0884.35013MR1464532
- [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. Biosciences31 (1976), pp 307-315. Zbl0333.35048MR682241
- [29] Vega ( J.-M.). — Multidimensional travelling fronts in a model from combustion theory and related problems, Diff. Int. Eq.6 (1993), pp 131-155. Zbl0786.35080MR1190170
- [30] Vega ( J.-M.). — On the uniqueness of multidimensional travelling fronts of some semilinear equations, J. Math. Anal. Appl.177 (1993), pp 481-490. Zbl0816.35035MR1231495
- [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. MR1103328
- [32] Volpert ( A.I.), Volpert ( V.A.), Volpert ( V.A.). - Traveling wave solutions of parabolic systems, Translations of Math. Monographs140, Amer. Math. Soc., 1994. Zbl1001.35060MR1297766
- [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. Zbl0727.35070MR1129338
- [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. Zbl0769.35033MR1129560
- [36] Zeldovich ( J.B.), Frank-Kamenetskii ( D.A.). - A theory of thermal propagation of flame, Acta Physiochimica URSS9 (1938), pp 341-350. English translation: in Dynamics of curved fronts, R. Pelcé Ed., Perspectives in Physics Series, Academic Press, New York1988, pp 131-140.
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