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Volumn 110, Issue 16, 2006, Pages 5235-5256

Low-dimensional manifolds in reaction-diffusion equations. 1. Fundamental aspects

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED DOMAINS; INFINITE DIMENSIONS; PARABOLIC SYSTEMS; REACTION-DIFFUSION EQUATIONS;

EID: 33646408129     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp055592s     Document Type: Article
Times cited : (33)

References (70)
  • 10
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    • Texts in Applied Mathematics 20; Springer-Verlag: New York
    • (c) Holmes, M. H. Introduction to Perturbation Methods; Texts in Applied Mathematics 20; Springer-Verlag: New York, 1995.
    • (1995) Introduction to Perturbation Methods
    • Holmes, M.H.1
  • 26
    • 0037700455 scopus 로고    scopus 로고
    • and references therein
    • For recent developments and important applications, for example, see: Valorani, M.; Najm, H. N.; Goussis, D. A. Combust. Flame 2003, 134, 35 and references therein.
    • (2003) Combust. Flame , vol.134 , pp. 35
    • Valorani, M.1    Najm, H.N.2    Goussis, D.A.3
  • 30
    • 0000998102 scopus 로고
    • Recent applications and algorithm developments concerning the Maas-Pope algorithm by Maas and co-workers can be found in: (a) Maas, U. Appl. Math. 1995, 3, 249.
    • (1995) Appl. Math. , vol.3 , pp. 249
    • Maas, U.1
  • 37
    • 0029256799 scopus 로고
    • Other recent applications and algorithm developments of the Maas-Pope algorithm can be found, for example, in: (a) Eggels, R. L. G. M.; de Goey, L. P. H. Combust. Flame 1995, 700, 559.
    • (1995) Combust. Flame , vol.700 , pp. 559
    • Eggels, R.L.G.M.1    De Goey, L.P.H.2
  • 63
    • 0004245694 scopus 로고
    • Abramowitz, M., Stegun, I. A., Eds.; Dover: New York
    • Handbook of Mathematical Functions; Abramowitz, M., Stegun, I. A., Eds.; Dover: New York, 1965.
    • (1965) Handbook of Mathematical Functions
  • 64
    • 33646427136 scopus 로고    scopus 로고
    • note
    • Local linearity stability analysis for ordinary differential equations is discussed in many places. For example, see ref 22.
  • 65
    • 33646430781 scopus 로고    scopus 로고
    • note
    • Chapter 5.3 of ref 27 has a discussion of the stability analysis of partial differential equations.
  • 66
    • 0003991043 scopus 로고    scopus 로고
    • Cambridge University Press: Cambridge, U. K.
    • Discussions of local linear stability analysis are less common for partial differential equations, but the generation and use of the linearization is an important part of numerical methods centered on semidiscrete methods. See, for example, ref 31 or Iserles, A. A First Course in the Numerical Analysis of Differential Equations; Cambridge University Press: Cambridge, U. K., 1996.
    • (1996) A First Course in the Numerical Analysis of Differential Equations
  • 67
    • 0004236492 scopus 로고    scopus 로고
    • Johns Hopkins University Press: Baltimore, MD
    • For example, see: Golub G. H.; Van Loan, C. F. Matrix Computations; Johns Hopkins University Press: Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 70
    • 0001811061 scopus 로고
    • Stepleman, R. S. et al., Eds.; North-Holland: Amsterdam
    • Hindmarsh, A. C. In Scientific Computing; Stepleman, R. S. et al., Eds.; North-Holland: Amsterdam, 1983; p 55.
    • (1983) Scientific Computing , pp. 55
    • Hindmarsh, A.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.