Spectral analysis of traveling waves for nonlocal evolution equations

SIAM Journal on Mathematical Analysis

Volumn 38, Issue 1, 2006, Pages 116-126

  Bates, Peter W ^a   Chen, Fengxin ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

Continuation; Nonlocal phase transition; Travelling waves

Indexed keywords

CONTINUATION; NONLOCAL PHASE TRANSITION; TRAVELING WAVES;

ASYMPTOTIC STABILITY; LINEARIZATION; SPECTRUM ANALYSIS;

WAVE EQUATIONS;

EID: 33847283443     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141004443968     Document Type: Article

References (20)

1. P. W. BATES AND F. CHEN, Periodic traveling wave solutions of an integrodifferential model for phase transition, Electron. J. Differential Equations, 26 (1999), pp. 1-19.
2. P. W. BATES, F. CHEN, AND J. WANG, Global existence and uniqueness of solutions to a non-local phase-field system, in US-Chinese Conference on Differential Equations and Applications, P. W. Bates, S.-N. Chow, K. Lu and X. Pan, eds., International Press, Cambridge, MA, 1997, pp. 14-21.
3. P. W. BATES, X. CHEN, AND A. CHMAJ, Equilibria and traveling waves for bistable equations with non-local and discrete dissipation, in Nonlinear Diffusive Systems - Dynamics and Asymptotics, E. Yanagida and Y. Morita, eds., RIMS, Kyoto, Japan, 2001, pp. 48-71.
4. P. W. BATES AND A. CHMAJ, An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions, J. Statist. Phys., 95 (1999), pp. 1119-1139.
5. P. W. BATES, P. C. FIFE, R. A. GARDNER, AND C. K. R. T. JONES, The existence of traveling wave solutions of a generalized phase-field model, SIAM J. Math. Anal., 28 (1997), pp. 60-93.
6. P. W. BATES, P. C. FIFE, X. REN, AND X. WANG, Traveling waves in a nonlocal model of phase transitions, Arch. Ration. Mech. Anal. 138 (1997), pp. 105-136.
7. P. W. BATES AND C. K. R. T. JONES, Invariant Manifolds for Semilinear Partial Differential Equations, in Dynam. Report. Ser. Dynam. Systems Appl. 2, Wiley, Chichester, UK, 1989, pp. 1-38.
8. P. W. BATES, K. LU, AND C. ZENG, Existence and persistence of invariant manifolds for semiflows in banach space, Mem. Amer. Math. Soc., 135 (1998).
9. P. W. BATES, K. LU, AND C. ZENG, Invariant foliations for semiflows near a normally hyperbolic invariant manifold, Trans. Amer. Math. Soc., 352 (2000), pp. 4641-4676.
10. P. W. BATES, K. LU, AND C. ZENG, Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., 52 (1999), pp. 983-1046.
11. F. CHEN, Almost periodic traveling waves of nonlocal evolution equations, Nonlinear Anal., 50 (2002), pp. 807-838.
12. X. CHEN, Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations, 2 (1997), pp. 125-160.
13. Z. CHEN, B. ERMENTROUT, AND B. MCLEOD, Traveling fronts for a class of non-local convolution differential equations. Appl. Anal., 64 (1997), pp. 235-253.
14. K. DEIMLING, Nonlinear Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985.
15. A. DE MASI, E. ORLANDI, E. PRESUTTI, AND L. TRIOLO, Stability of the interface in a model of phase separation, Proc. Roy. Soc. Edinburgh, 124 (1994), pp. 1013-1022.
16. B. ERMENTROUT AND J. B. MCLEOD, Existence and uniqueness of traveling waves for a neural network, Proc. Roy. Soc. Edinburgh, 123 (1993), pp. 461-478.
17. P. C. FIFE AND J. B. MCLEOD, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), pp. 335-361.
18. P. C. FIFE AND X. WANG, A convolution model for interfacial motion: The generation and propagation of internal layers in higher space dimensions, Adv. Differential Equations, 3 (1998), pp. 85-110.
19. A. FRIEDMAN, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
20. D. HENRY, Geometric theory of semilinear parabolic equations, in Lecture Notes in Math. 840, Springer-Verlag, New York, 1981.