@article{AIHPC_2004__21_3_319_0, author = {Bonheure, Denis}, title = {Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {319--340}, publisher = {Elsevier}, volume = {21}, number = {3}, year = {2004}, doi = {10.1016/j.anihpc.2003.03.001}, mrnumber = {2068305}, zbl = {1073.34044}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.03.001/} }
TY - JOUR AU - Bonheure, Denis TI - Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 319 EP - 340 VL - 21 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2003.03.001/ DO - 10.1016/j.anihpc.2003.03.001 LA - en ID - AIHPC_2004__21_3_319_0 ER -
%0 Journal Article %A Bonheure, Denis %T Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 319-340 %V 21 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2003.03.001/ %R 10.1016/j.anihpc.2003.03.001 %G en %F AIHPC_2004__21_3_319_0
Bonheure, Denis. Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 3, pp. 319-340. doi : 10.1016/j.anihpc.2003.03.001. http://www.numdam.org/articles/10.1016/j.anihpc.2003.03.001/
[1] Sobolev Spaces, Academic Press, 1975. | MR | Zbl
,[2] Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation, Calc. Var. Partial Differential Equations 17 (2003) 341-356. | MR | Zbl
, , , ,[3] D. Bonheure, P. Habets, L. Sanchez, Minimizers for fourth order symmetric bistable equation, Atti de seminari de matematica e fisica de la universita di Modena, in press.
[4] Analyse fonctionnelle, Théorie et applications, Masson, 1983. | MR | Zbl
,[5] Bistable systems with propagating fronts leading to patern formation, Phys. Rev. Lett. 60 (1988) 2641-2644.
, ,[6] Phase Transitions and Critical Phenomena, Academic Press, 1994.
, ,[7] Heteroclinics for a class of fourth order conservative differential equations, in: CD ROM Proceedings, Equadiff 10, Prague, 2001.
, , , ,[8] Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria, Comm. Math. Phys. 193 (1998) 337-371. | MR | Zbl
, , ,[9] Multitransition homoclinic and heteroclinic solutions of the extended Fisher-Kolmogorov equation, J. Differential Equations 131 (1996) 209-228. | MR | Zbl
, ,[10] Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Univ. Moskow Ser. Internat. Sec. A 1 (1937) 1-25. | Zbl
, , ,[11] Spatial patterns described by the extended Fisher-Kolmogorov (EFK) equation: Kinks, Differential Integral Equations 8 (1995) 1279-1304. | MR | Zbl
, ,[12] A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation, Topological Methods Nonlin. Anal. 6 (1995) 331-355. | MR | Zbl
, ,[13] Spatial Patterns, Higher Order Models in Physics and Mechanics, Birkhäuser, 2001. | MR | Zbl
, ,[14] Stationary solutions of a fourth-order nonlinear diffusion equation, Differentsial'nye Uravneniya 31 (2) (1995) 327-337. | MR | Zbl
, , ,[15] Homoclinic solutions for Swift-Hohenberg and suspension bridges type equations, J. Differential Equations 184 (1) (2002) 78-96. | MR | Zbl
, ,[16] Hydrodynamic fluctuations at the convective instability, Phys. Rev. A 51 (1977) 319-328.
, ,[17] J.B. van den Berg, Branches of heteroclinic, homoclinic and periodic solutions in a fourth-order bi-stable system, a numerical study, Master Thesis, Leiden University, October 1996.
[18] The phase plane picture for a class of fourth order conservative differential equations, J. Differential Equations 161 (2000) 110-153. | MR | Zbl
,[19] Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation, Arch. Rational Mech. Anal. 158 (2) (2001) 91-153. | MR | Zbl
, , ,[20] J.B. van den Berg, Dynamics and equilibria of fourth order differential equations, Ph.D. Thesis, Leiden University, December 2000. | Zbl
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