Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
Annales de l'I.H.P. Analyse non linéaire (2004)
- Volume: 21, Issue: 3, page 319-340
- ISSN: 0294-1449
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top- [1] Adams R.A., Sobolev Spaces, Academic Press, 1975. Zbl0314.46030MR450957
- [2] Bonheure D., Sanchez L., Tarallo M., Terracini S., Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation, Calc. Var. Partial Differential Equations17 (2003) 341-356. Zbl1031.34043MR1993958
- [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. Zbl1115.34040
- [4] Brezis H., Analyse fonctionnelle, Théorie et applications, Masson, 1983. Zbl0511.46001MR697382
- [5] Dee G.T., van Saarloos W., Bistable systems with propagating fronts leading to patern formation, Phys. Rev. Lett.60 (1988) 2641-2644.
- [6] Gomper G., Schick M., Phase Transitions and Critical Phenomena, Academic Press, 1994.
- [7] Habets P., Sanchez L., Tarallo M., Terracini S., Heteroclinics for a class of fourth order conservative differential equations, in: CD ROM Proceedings, Equadiff 10, Prague, 2001.
- [8] Kalies W.D., Kwapisz J., VanderVorst R.C.A.M., Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria, Comm. Math. Phys.193 (1998) 337-371. Zbl0908.34034MR1618147
- [9] Kalies W.D., VanderVorst R.C.A.M., Multitransition homoclinic and heteroclinic solutions of the extended Fisher–Kolmogorov equation, J. Differential Equations131 (1996) 209-228. Zbl0872.34033MR1419012
- [10] Kolmogorov A., Petrovski I., Piscounov N., 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. A1 (1937) 1-25. Zbl0018.32106
- [11] Peletier L.A., Troy W.C., Spatial patterns described by the extended Fisher–Kolmogorov (EFK) equation: Kinks, Differential Integral Equations8 (1995) 1279-1304. Zbl0826.34056MR1329841
- [12] Peletier L.A., Troy W.C., A topological shooting method and the existence of kinks of the extended Fisher–Kolmogorov equation, Topological Methods Nonlin. Anal.6 (1995) 331-355. Zbl0862.34030MR1399544
- [13] Peletier L.A., Troy W.C., Spatial Patterns, Higher Order Models in Physics and Mechanics, Birkhäuser, 2001. Zbl1076.34515MR1839555
- [14] Peletier L.A., Van der Vorst R.K.A.M., Troy W.C., Stationary solutions of a fourth-order nonlinear diffusion equation, Differentsial'nye Uravneniya31 (2) (1995) 327-337. Zbl0856.35029MR1373793
- [15] Smets D., van den Berg J.B., Homoclinic solutions for Swift–Hohenberg and suspension bridges type equations, J. Differential Equations184 (1) (2002) 78-96. Zbl1029.34036MR1929147
- [16] Swift J.B., Hohenberg P.C., Hydrodynamic fluctuations at the convective instability, Phys. Rev. A51 (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] van den Berg J.B., The phase plane picture for a class of fourth order conservative differential equations, J. Differential Equations161 (2000) 110-153. Zbl0952.34026MR1740359
- [19] van den Berg G.J.B., Peletier L.A., Troy W.C., Global branches of multi-bump periodic solutions of the Swift–Hohenberg equation, Arch. Rational Mech. Anal.158 (2) (2001) 91-153. Zbl0983.34032MR1838655
- [20] J.B. van den Berg, Dynamics and equilibria of fourth order differential equations, Ph.D. Thesis, Leiden University, December 2000. Zbl1136.37301