@article{AIHPC_2008__25_2_381_0,
author = {Risler, Emmanuel},
title = {Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {381--424},
year = {2008},
publisher = {Elsevier},
volume = {25},
number = {2},
doi = {10.1016/j.anihpc.2006.12.005},
mrnumber = {2400108},
zbl = {1152.35047},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.12.005/}
}
TY - JOUR AU - Risler, Emmanuel TI - Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 381 EP - 424 VL - 25 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2006.12.005/ DO - 10.1016/j.anihpc.2006.12.005 LA - en ID - AIHPC_2008__25_2_381_0 ER -
%0 Journal Article %A Risler, Emmanuel %T Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 381-424 %V 25 %N 2 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2006.12.005/ %R 10.1016/j.anihpc.2006.12.005 %G en %F AIHPC_2008__25_2_381_0
Risler, Emmanuel. Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 381-424. doi: 10.1016/j.anihpc.2006.12.005
[1] A. Ambrosetti, M.L. Bertotti, Homoclinics for second order conservative systems, in: M. Miranda (Ed.), PDE's and Related Subjects, Trento, Italy, 1990, in: Pitman Res. Notes Math. Ser., vol. 269, 1992, pp. 21-37. | Zbl | MR
[2] , , Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002) 949-1032. | Zbl | MR
[3] , , , Multi-dimensional traveling wave solutions of a flame propagation model, Arch. Rat. Mech. Anal. 111 (1990) 33-49. | Zbl | MR
[4] , Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997) 125-160. | Zbl | MR
[5] , Bounded, locally compact global attractors for semilinear damped wave equations on , J. Diff. Int. Eq. 9 (1996) 1147-1156. | Zbl | MR
[6] , Long Time Behavior of Solutions of Bistable Nonlinear Diffusion Equations, Arch. Rat. Mech. Anal. 70 (1979) 31-46. | Zbl | MR
[7] , , The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335-361. | Zbl | MR
[8] , , A phase plane discussion of convergence to traveling fronts for nonlinear diffusion, Arch. Rat. Mech. Anal. 75 (1981) 281-314. | Zbl | MR
[9] , Convergence to traveling waves in damped hyperbolic equations, in: , , (Eds.), International Conference on Differential Equations, vol. 1, Berlin 1999, World Scientific, 2000, pp. 787-793. | Zbl | MR
[10] Th. Gallay, R. Joly, Global stability of travelling fronts for a damped wave equation with bistable nonlinearity, Preprint. | Zbl | MR | Numdam
[11] , , A variational proof of global stability for bistable traveling waves, Diff. Int. Equ. 20 (8) (2007) 901-926. | MR
[12] , , Energy flow in extended gradient partial differential equations, J. Dyn. Diff. Equ. 13 (2001) 4. | Zbl | MR
[13] , , The Cauchy problem in local spaces for the complex Ginzburg-Landau equation, II. Contraction methods, Comm. Math. Phys. 187 (1997) 45-79. | Zbl | MR
[14] , A variational approach to traveling waves, Technical Report 85, Max Planck Institute for Mathematical Sciences, Leipzig, 2001.
[15] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, 1981. | Zbl | MR
[16] , Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity, J. Diff. Equ. 144 (1998) 302-312. | Zbl | MR
[17] , The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rat. Mech. Anal. 58 (1975) 181-205. | Zbl | MR
[18] , The stable, center stable, center, center unstable and unstable manifolds, J. Diff. Equ. 3 (1967) 546-570. | Zbl | MR
[19] , , , A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bjul. Moskovskovo Gos. Univ. 17 (1937) 1-72.
[20] , The complex Ginzburg-Landau equation on large and unbounded domains: sharper bounds and attractors, Nonlinearity 10 (1997) 199-222. | Zbl | MR
[21] , , Attractors for modulation equations on unbounded domains - existence and comparison, Nonlinearity 8 (1995) 743-768. | Zbl | MR
[22] , A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type, Disc. Cont. Dyn. Syst. Ser. B 4 (2004) 867-892. | Zbl | MR
[23] , , Monotonicity and convergence results in order preserving systems in the presence of symmetry, Disc. Cont. Dyn. Syst. 5 (1999) 1-34. | Zbl | MR
[24] , , Stability analysis in order-preserving systems in the presence of symmetry, Proc. Roy. Soc. Edinburgh Sect. A 129 (2) (1999) 395-438. | Zbl | MR
[25] E. Risler, A global relaxation result for bistable solutions of spatially extended gradient-like systems in one unbounded spatial dimension, in preparation.
[26] E. Risler, Global behavior of bistable solutions of nonlinear parabolic systems with a gradient structure, in preparation.
[27] , Eventual monotonicity and convergence to traveling fronts for the solutions of parabolic equations in cylinders, Ann. Inst. H. Poincare Anal. Non Lineaire 14 (1997) 499-552. | Zbl | MR | Numdam
[28] , Multidimensional traveling fronts in a model from combustion theory and related problems, Diff. Int. Eq. 6 (1993) 131-155. | Zbl | MR
[29] , , , Traveling Wave Solutions of Parabolic Systems, Translations of Mathematical Monographs, vol. 140, AMS, Providence, RI, 1994. | Zbl | MR
[30] , Existence and uniqueness of traveling waves in a reaction-diffusion equation with combustion nonlinearity, Indiana Univ. Math. J. 40 (3) (1991) 985-1008. | Zbl | MR
Cité par Sources :





