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Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation
1. | CAMS - Ecole des Hautes Etudes en Sciences Sociales, 190-198 avenue de France, 75013 Paris, France |
References:
[1] |
P. W. Bates and F. Chen, Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation, J. Math. Anal. Appl., 273 (2002), 45-57.
doi: 10.1016/S0022-247X(02)00205-6. |
[2] |
P. W. Bates and F. Chen, Spectral analysis of traveling waves for nonlocal evolution equations, SIAM J. Math. Anal., 38 (2006), 116-126.
doi: 10.1137/S0036141004443968. |
[3] |
P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal., 138 (1997), 105-136.
doi: 10.1007/s002050050037. |
[4] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[5] |
F. Chen, Uniform stability if multidimensional travelling waves for the nonlocal Allen-Cahn equation, Electronic Journal of Differential Equations, 10 (2003), 109-113. |
[6] |
X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Advences in Differential Equations, 2 (1997), 125-160. |
[7] |
J. Coville, Equation de Réaction Diffusion Non-locale, Thèse de doctorat del'université Pierre et Marie Curie, Paris 6, 2003. |
[8] |
A. De Masi, T. Gobron and E. Presutti, Traveling fronts in non-local evolution equations, Arch. Rat. Mech. Anal, 132 (1995), 143-205.
doi: 10.1007/BF00380506. |
[9] |
G. B. Ermentrout and J. B. McLeod, Existence and uniqueness of travelling waves for a neural network, Proc. Roy. Soc. Edin., 123 (1993), 461-478.
doi: 10.1017/S030821050002583X. |
[10] |
T. Gallay and A. Scheel, Diffusive stability of oscillations in reaction-diffusion systems, Trans. Amer. Math. Soc., 363 (2011), 2571-2598.
doi: 10.1090/S0002-9947-2010-05148-7. |
[11] |
A. Hoffman, H. J. Hupkes and E. S. van Vleck, Multi-dimensional stability of waves travelling through rectangular lattices in rational directions, Trans. Amer. Math. Soc., 367 (2015), 8757-8808.
doi: 10.1090/S0002-9947-2015-06392-2. |
[12] |
M. A. Johnson and K. Zumbrun, Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case, J. Differential Equations, 249 (2010), 1213-1240.
doi: 10.1016/j.jde.2010.04.015. |
[13] |
T. Kapitula, Multidimensional stability of planar traveling waves, Trans. Amer. Math. Soc., 349 (1997), 257-269.
doi: 10.1090/S0002-9947-97-01668-1. |
[14] |
C. D. Levermore and J. X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, II, Comm. in Par. Diff. Equ., 17 (1992), 1901-1924.
doi: 10.1080/03605309208820908. |
[15] |
H. Matano, M. Nara and M. Taniguchi, Stability of planar waves in the Allen-Cahn equation, Comm. in Par. Diff. Equ., 34 (2009), 976-1002.
doi: 10.1080/03605300902963500. |
[16] |
J. R. Miller and H. Zeng, Multidimensional stability of planar traveling waves for an integrodifference model, Discrete and Continuous Dynamical Systems B, 18 (2013), 741-751. |
[17] |
M. Oh and K. Zumbrun, Stability and asymptotic behavior of traveling-wave solutions of viscous conservation laws in several dimensions, Arch. Ration. Mech. Anal., 196 (2010), 1-20.
doi: 10.1007/s00205-009-0229-6. |
[18] |
J. X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, I, Comm. in Par. Diff. Equ., 17 (1992), 1889-1899.
doi: 10.1080/03605309208820907. |
show all references
References:
[1] |
P. W. Bates and F. Chen, Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation, J. Math. Anal. Appl., 273 (2002), 45-57.
doi: 10.1016/S0022-247X(02)00205-6. |
[2] |
P. W. Bates and F. Chen, Spectral analysis of traveling waves for nonlocal evolution equations, SIAM J. Math. Anal., 38 (2006), 116-126.
doi: 10.1137/S0036141004443968. |
[3] |
P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal., 138 (1997), 105-136.
doi: 10.1007/s002050050037. |
[4] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[5] |
F. Chen, Uniform stability if multidimensional travelling waves for the nonlocal Allen-Cahn equation, Electronic Journal of Differential Equations, 10 (2003), 109-113. |
[6] |
X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Advences in Differential Equations, 2 (1997), 125-160. |
[7] |
J. Coville, Equation de Réaction Diffusion Non-locale, Thèse de doctorat del'université Pierre et Marie Curie, Paris 6, 2003. |
[8] |
A. De Masi, T. Gobron and E. Presutti, Traveling fronts in non-local evolution equations, Arch. Rat. Mech. Anal, 132 (1995), 143-205.
doi: 10.1007/BF00380506. |
[9] |
G. B. Ermentrout and J. B. McLeod, Existence and uniqueness of travelling waves for a neural network, Proc. Roy. Soc. Edin., 123 (1993), 461-478.
doi: 10.1017/S030821050002583X. |
[10] |
T. Gallay and A. Scheel, Diffusive stability of oscillations in reaction-diffusion systems, Trans. Amer. Math. Soc., 363 (2011), 2571-2598.
doi: 10.1090/S0002-9947-2010-05148-7. |
[11] |
A. Hoffman, H. J. Hupkes and E. S. van Vleck, Multi-dimensional stability of waves travelling through rectangular lattices in rational directions, Trans. Amer. Math. Soc., 367 (2015), 8757-8808.
doi: 10.1090/S0002-9947-2015-06392-2. |
[12] |
M. A. Johnson and K. Zumbrun, Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case, J. Differential Equations, 249 (2010), 1213-1240.
doi: 10.1016/j.jde.2010.04.015. |
[13] |
T. Kapitula, Multidimensional stability of planar traveling waves, Trans. Amer. Math. Soc., 349 (1997), 257-269.
doi: 10.1090/S0002-9947-97-01668-1. |
[14] |
C. D. Levermore and J. X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, II, Comm. in Par. Diff. Equ., 17 (1992), 1901-1924.
doi: 10.1080/03605309208820908. |
[15] |
H. Matano, M. Nara and M. Taniguchi, Stability of planar waves in the Allen-Cahn equation, Comm. in Par. Diff. Equ., 34 (2009), 976-1002.
doi: 10.1080/03605300902963500. |
[16] |
J. R. Miller and H. Zeng, Multidimensional stability of planar traveling waves for an integrodifference model, Discrete and Continuous Dynamical Systems B, 18 (2013), 741-751. |
[17] |
M. Oh and K. Zumbrun, Stability and asymptotic behavior of traveling-wave solutions of viscous conservation laws in several dimensions, Arch. Ration. Mech. Anal., 196 (2010), 1-20.
doi: 10.1007/s00205-009-0229-6. |
[18] |
J. X. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation, I, Comm. in Par. Diff. Equ., 17 (1992), 1889-1899.
doi: 10.1080/03605309208820907. |
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