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Wavespeed selection in the heterogeneous Fisher equation: Slowly varying inhomogeneity
1. | School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom |
References:
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J. K. Cohen and R. M. Lewis, A ray method for the asymptotic solution of the diffusion equation, IMA J. Appl. Math., 3 (1967), 266-290.
doi: 10.1093/imamat/3.3.266. |
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C. M. Cuesta and J. R. King, Front propagation a heterogeneous Fisher equation: The homogeneous case is non-generic, Q. J. Mech. Appl. Math., 63 (2010), 521-571.
doi: 10.1093/qjmam/hbq017. |
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U. Ebert and W. van Saarloos, Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts, Physica D, 146 (2000), 1-99.
doi: 10.1016/S0167-2789(00)00068-3. |
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L. C. Evans and P. E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations, Indiana Uni. Math. J., 38 (1989), 141-172.
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J. Smoller, "Linear Elastic Waves," Cambridge University Press, 2001.
doi: 10.1017/CBO9780511755415. |
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M. Freidlin, Limit theorems for large deviations and reaction-diffusion equations, Ann. Prob., 13 (1985), 639-675.
doi: 10.1214/aop/1176992901. |
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John King, "Mathematical Aspects of Semiconductor Process Modelling," DPhil Thesis, University of Oxford. 1986. |
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J. R. King, High concentration arsenic diffusion in crystalline silicon: An asymptotic analysis, IMA J. Appl. Math., 38 (1987), 87-95.
doi: 10.1093/imamat/38.2.87. |
[9] |
V. Méndez, J. Fort, H. G. Rotstein and S. Fedotov, Speed of reaction-diffusion fronts in spatially heterogeneous media, Phys. Rev. E, 68 (2003), 041105.
doi: 10.1103/PhysRevE.68.041105. |
[10] |
A. I. Volpert, V. A. Volpert and V. A. Volpert, "Traveling Wave Solutions of Parabolic Systems," American Mathematical Society, 1994. |
[11] |
J. Xin, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), 161-230.
doi: 10.1137/S0036144599364296. |
show all references
References:
[1] |
J. K. Cohen and R. M. Lewis, A ray method for the asymptotic solution of the diffusion equation, IMA J. Appl. Math., 3 (1967), 266-290.
doi: 10.1093/imamat/3.3.266. |
[2] |
C. M. Cuesta and J. R. King, Front propagation a heterogeneous Fisher equation: The homogeneous case is non-generic, Q. J. Mech. Appl. Math., 63 (2010), 521-571.
doi: 10.1093/qjmam/hbq017. |
[3] |
U. Ebert and W. van Saarloos, Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts, Physica D, 146 (2000), 1-99.
doi: 10.1016/S0167-2789(00)00068-3. |
[4] |
L. C. Evans and P. E. Souganidis, A PDE approach to geometric optics for certain semilinear parabolic equations, Indiana Uni. Math. J., 38 (1989), 141-172.
doi: 10.1512/iumj.1989.38.38007. |
[5] |
J. Smoller, "Linear Elastic Waves," Cambridge University Press, 2001.
doi: 10.1017/CBO9780511755415. |
[6] |
M. Freidlin, Limit theorems for large deviations and reaction-diffusion equations, Ann. Prob., 13 (1985), 639-675.
doi: 10.1214/aop/1176992901. |
[7] |
John King, "Mathematical Aspects of Semiconductor Process Modelling," DPhil Thesis, University of Oxford. 1986. |
[8] |
J. R. King, High concentration arsenic diffusion in crystalline silicon: An asymptotic analysis, IMA J. Appl. Math., 38 (1987), 87-95.
doi: 10.1093/imamat/38.2.87. |
[9] |
V. Méndez, J. Fort, H. G. Rotstein and S. Fedotov, Speed of reaction-diffusion fronts in spatially heterogeneous media, Phys. Rev. E, 68 (2003), 041105.
doi: 10.1103/PhysRevE.68.041105. |
[10] |
A. I. Volpert, V. A. Volpert and V. A. Volpert, "Traveling Wave Solutions of Parabolic Systems," American Mathematical Society, 1994. |
[11] |
J. Xin, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), 161-230.
doi: 10.1137/S0036144599364296. |
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