Invariant manifolds for parabolic partial differential equations on unbounded domains

Archive for Rational Mechanics and Analysis

Volumn 138, Issue 3, 1997, Pages 279-306

  Wayne, C Eugene ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; INVERSE PROBLEMS; SPECTRUM ANALYSIS;

INVARIANT MANIFOLDS; TRAVELING WAVE; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS; UNBOUNDED DOMAINS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031282918     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050042     Document Type: Article

References (33)

1. BRESSAN, A., 1992, Stable blow-up patterns. J. Diff. Eqs. 98, 57-75.
2. BERBENES, J. & BRICHER, S., 1992, Final time blow up profiles for semilinear parabolic equations via center manifold theory. SIAM J. Math. Anal. 23, 852-869.
3. BATES, P. & JONES, C., 1989, Invariant manifolds for semilinear partial differential equations. Dynamics Reported 2, 1-38.
4. BRICMONT, J. & KUPIANEN, A., 1996, Stable non-gaussian diffusive profiles. Nonlinear Anal. 26, 583-593.
5. BRICMONT, J., KUPIAINEN, A. & LIN, G., 1994, Renormalization group and asymptotics of solutions of nonlinear parabolic equations. Comm. Pure Appl. Math. 47, 893-922.
6. BREZIS, H., PELETIER, L. A., & TERMAN, D., 1986, A very singular solution of the heat equation with absorption. Arch. Rational. Mech. Anal. 95, 185-209.
7. BONA, J., PROMISLOW, K., & WAYNE, C. E., 1995, Higher-order asymptotics of decaying solutions of some nonlinear dispersive, dissipative wave equations. Non-linearity 8 1179-1206.
8. CARR, J., 1983, The Centre Manifold Theorem and its Applications, Springer-Verlag, New York.
9. CARR, J. & MUNCASTER, R. G., 1983, The application of centre manifolds to amplitude expansions. II. Infinite dimensional problems. J. Diff. Eqs. 50, 260-279.
10. ESCOBEDO, M. & KAVIAN, O., 1988 Asymptotic behaviour of positive solutions of a nonlinear heat equation. Houston J. Math. 14, 39-50.
11. ESCOBEDO, M., KAVIAN, O. & MATANO, H., 1995, Large time behavior of solutions of a dissipative semi-linear heat equation. Comm. Partial Diff. Eqs. 20, 1427-1452.
12. ECKMANN, J.-P. & WAYNE. C. E., 1991, Propagating fronts and the center manifold theorem. Comm. Math. Phys. 136, 285-307.
13. p. Comm. Pure Appl. Math. 45, 821-869.
14. FOIAS, C. & SAUT, J.-C., 1984, On the smoothness of the nonlinear spectral manifolds associated to the Navier-Stokes equations. Indiana Univ. Math. J. 33, 911-926.
15. GALAKTIONOV, V. A., KUDYMOV, S. P., & SAMARSKII, A. A., 1986, On asymptotic $eigenfunctions$ of the Cauchy problem for a nonlinear parabolic equation. Math. USSR Sbornik 54, 421-455.
16. GALLAY, T., 1993. A center-stable manifold theorem for differential equations in banach space. Comm. Math. Phys. 152, 249-268.
17. GIGA, Y. & KOHN, R., 1987, Characterizing blow-up using similarity variables. Indiana Univ. Math. J. 36, 1-40.
18. GLIMM, J. & JAFFE A., 1981, Quantum Physics, Springer-Verlag, New York.
19. HENRY, D., 1981, Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes in Mathematics 840, New York.
20. KAPITULA, T., 1994. On the stability of travelling waves in weighted L∞ spaces. J. Diff. Eqs. 112, 179-215.
21. KAMIN, S. & PELETIER, L. A., 1985, Large time behaviour of solutions of the heat equation with absorption. Proc. Amer. Math. Soc. 95, 393-408.
22. KIRCHGÄSSNER, K., 1988, Nonlinearly resonant surface waves, and homoclinic bifurcation. Adv. Appl. Mech. 26, 135-181.
23. DE LA LLAVE, R. & WAYNE, C. E., 1995, On Irwin's proof of the invariant manifold theorem. Math. Z. 219, 301-321.
24. MIELKE, A., 1986, Steady flows of inviscid flows under localized perturbations. J. Diff. Eqs. 65, 89-116.
25. MIELKE, A., 1991, Locally invariant manifolds for quasilinear parabolic equations. Rocky Mountain J. Math. 21, 707-714.
26. PEGO, R. & WEINSTEIN, M., 1994, Asymptotic stability of solitary waves. Comm. Math. Phys. 164, 305-349.
27. RUELLE, D., 1989, Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press.
28. SATTINGER, D., 1976, On the stability of waves of nonlinear parabolic systems. Adv. in Math. 22, 312-357.
29. STRAUSS, W., 1974, Dispersion of low-energy waves for two conservative equations Arch. Rational. Mech. Anal. 55, 86-92.
30. SOFFER, A. & WEINSTEIN, M., 1991. Multichannel nonlinear scattering for non-integrable equations. Comm. Math. Phys. 44, 573-604.
31. VALENT, T., 1988, Boundary Value Problems of Finite Elasticity, Springer-Verlag, New York.
32. VISHIK, M., 1992, Asymptotic Behaviour of Solutions of Evolutionary Equations, Cambridge Univ. Press, Cambridge.
33. VANDERBAUWHEDE, A. & Iooss, G., 1992, Center manifold theory in infinite dimensions. Dynamics Reported, New Series, 1, 125-163.