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Communications on Pure and Applied Analysis (CPAA)
 

Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion
Pages: 275 - 305, Issue 1, January 2012

doi:10.3934/cpaa.2012.11.275      Abstract        References        Full text (6044.4K)           Related Articles

Kota Ikeda - Graduate School of Advanced Mathematical Science, Meiji University, Kawasaki, 214-8571, Japan (email)
Masayasu Mimura - Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571, Japan (email)

1 D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial differential equations and related topics, Lecture Notes in Math., Springer, 446 (1975), 5-49.       
2 A. Fasano, M. Mimura and M. Primicerio, Modelling a slow smoldering combustion process, Mathematical Methods in the Applied Science, 33 (2010), 1211-1220.       
3 A. Fasano, H. Izuhara, M. Mimura and M. Primicerio, Traveling wave solutions in a simplified smoldering combustion model, manuscript.
4 D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin, 1981.       
5 K. Ikeda and M. Mimura, Mathematical treatment of a model for smoldering combustion, Hiroshima Math. J., 38 (2008), 349-361.       
6 C. K. R. T. Jones, Geometric singular perturbation theory, Dynamical systems (Montecatini Terme, 1994), Lecture Notes in Math., Springer, Berlin, 1609 (1995), 44-118.       
7 A. Lunardi, Analytic semigroups and optimal regularity in parabolic problems, Birkhäuser Verlag, 1995.       
8 S. L. Olson, H. R. Baum and T. Kashiwagi, Finger-like smoldering over thin cellulosic sheets in microgravity, The Combustion Institute, (1998), 2525-2533.
9 A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer-Verlag, New York, 44, 1983.       
10 L. Roques, Study of the premixed flame model with heat losses. The existence of two solutions, European J. Appl. Math., 16 (2005), 741-765.       
11 E. Yanagida, Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), 81-104.       
12 O. Zik, Z. Olami and E.Moses, Fingering instability in combustion, Phys. Rev. Lett., 81 (1998), 3868-3871.

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