Keywords: Periodic traveling waves, Nonlinear stability, Bloch decomposition

@article{AIHPC_2011__28_4_471_0, author = {Johnson, Mathew A. and Zumbrun, Kevin}, title = {Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction--diffusion equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {28}, number = {4}, year = {2011}, pages = {471-483}, doi = {10.1016/j.anihpc.2011.05.003}, zbl = {1246.35034}, mrnumber = {2823880}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2011__28_4_471_0} }

Johnson, Mathew A.; Zumbrun, Kevin. Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction–diffusion equations. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 4, pp. 471-483. doi : 10.1016/j.anihpc.2011.05.003. http://www.numdam.org/item/AIHPC_2011__28_4_471_0/

[1] The dynamics of modulated wavetrains, Mem. Amer. Math. Soc. 199 no. 934 (2009) | MR 2507940

, , , ,[2] On the structure of the spectra of periodic traveling waves, J. Math. Pures Appl. 72 (1993), 415-439 | MR 1239098 | Zbl 0831.35077

,[3] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., Springer-Verlag, Berlin (1981) | MR 610244 | Zbl 0456.35001

,[4] Nonlinear stability of periodic traveling waves of viscous conservation laws in the generic case, J. Differential Equations 249 no. 5 (2010), 1213-1240 | MR 2652171 | Zbl 1198.35027

, ,[5] Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg (1985) | MR 407617

,[6] Stability and diffusive dynamics on extended domains, Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, Springer, Berlin (2001), 563-583 | MR 1850322 | Zbl 1004.35018

, , ,[7] Stability and asymptotic behavior of traveling-wave solutions of viscous conservation laws in several dimensions, Arch. Ration. Mech. Anal. 196 no. 1 (2010), 1-20, Arch. Ration. Mech. Anal. 196 no. 1 (2010), 21-23 | MR 2601067 | Zbl 1197.35075

, ,[8] Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. vol. 44, Springer-Verlag, New York, Berlin (1983) | MR 710486 | Zbl 0516.47023

,[9] B. Sandstede, A. Scheel, G. Schneider, H. Uecker, Diffusive mixing of periodic wave trains in reaction–diffusion systems with different phases at infinity, draft, 2010. | MR 2876664

[10] Nonlinear diffusive stability of spatially periodic solutions – abstract theorem and higher space dimensions, Proceedings of the International Conference on Asymptotics in Nonlinear Diffusive Systems, Sendai, 1997, Tohoku Math. Publ. vol. 8, Tohoku Univ., Sendai (1998), 159-167 | MR 1617491 | Zbl 0907.35015

,[11] Diffusive stability of rolls in the two-dimensional real and complex Swift–Hohenberg equation, Comm. Partial Differential Equations 24 no. 11–12 (1999), 2109-2146 | MR 1720762 | Zbl 0937.35135

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