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Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion
1. | Graduate School of Advanced Mathematical Science, Meiji University, Kawasaki, 214-8571 |
2. | Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571 |
References:
[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.
doi: 10.1007/BFb0070595. |
[2] |
A. Fasano, M. Mimura and M. Primicerio, Modelling a slow smoldering combustion process, Mathematical Methods in the Applied Science, 33 (2010), 1211-1220.
doi: 10.1002/mma.1301. |
[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.
doi: 10.1007/BFb0095239. |
[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.
doi: 10.1016/S0082-0784(98)80104-5. |
[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.
doi: 10.1017/S0956792505006431. |
[11] |
E. Yanagida, Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), 81-104.
doi: 10.1007/BF00276548. |
[12] |
O. Zik, Z. Olami and E.Moses, Fingering instability in combustion, Phys. Rev. Lett., 81 (1998), 3868-3871.
doi: 10.1103/PhysRevLett.81.3868. |
show all references
References:
[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.
doi: 10.1007/BFb0070595. |
[2] |
A. Fasano, M. Mimura and M. Primicerio, Modelling a slow smoldering combustion process, Mathematical Methods in the Applied Science, 33 (2010), 1211-1220.
doi: 10.1002/mma.1301. |
[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.
doi: 10.1007/BFb0095239. |
[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.
doi: 10.1016/S0082-0784(98)80104-5. |
[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.
doi: 10.1017/S0956792505006431. |
[11] |
E. Yanagida, Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), 81-104.
doi: 10.1007/BF00276548. |
[12] |
O. Zik, Z. Olami and E.Moses, Fingering instability in combustion, Phys. Rev. Lett., 81 (1998), 3868-3871.
doi: 10.1103/PhysRevLett.81.3868. |
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