×

Bifurcation and stability in a chemical system. (English) Zbl 0355.35009


MSC:

35B35 Stability in context of PDEs
35B45 A priori estimates in context of PDEs
35J60 Nonlinear elliptic equations
35G20 Nonlinear higher-order PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Auchmuty, J. F.G; Nicolis, G., Dissipative structures, catastrophes and pattern formation: a bifurcation analysis, (Proc. Nat. Acad. Sci. U.S.A., 71 (1974)), 2748-2751 · Zbl 0303.76045
[2] J. F. G. Auchmuty and G. NicolisBull. Math. Biol.; J. F. G. Auchmuty and G. NicolisBull. Math. Biol. · Zbl 0357.35048
[3] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12, 623-727 (1959) · Zbl 0093.10401
[4] Brezis, D., Perturbations singulières et problèmes d’évolution avec défaut d’ajuste-ment, C. R. Acad. Sci. Paris, 276, 1597-1600 (1973) · Zbl 0257.46030
[5] Herschkowitz-Kaufman, M.; Nicolis, G., Localized spatial structures and non-linear chemical waves in dissipative structures, J. Chem. Phys., 56, 1890-1895 (1972)
[6] M. Herschkowitz-KaufmanBull. Math. Biol.; M. Herschkowitz-KaufmanBull. Math. Biol. · Zbl 0324.92004
[7] Iooss, G., Bifurcation et stabilité, (Publications Mathématiques n∘ 31 (1973), Université Paris Sud: Université Paris Sud Orsay, France) · Zbl 0408.58019
[8] Iooss, G., Existence et stabilité de la solution périodique secondaire intervenant dans les problèmes d’évolution du type Navier-Stokes, Arch. Rational. Mech. Anal., 47, 301-332 (1972) · Zbl 0258.35057
[9] Kato, T., Perturbation Theory of Operators (1966), Springer-Verlag: Springer-Verlag Berlin · Zbl 0148.12601
[10] Lefever, R.; Prigogine, I., Symmetry breaking instabilities in dissipative systems, II, J. Chem. Phys., 48, 1695-1700 (1968)
[11] Lefever, R., (Thèse de Doctorat (1970), Chimie Physique, Université Libre de Bruxelles)
[12] Nicolis, G., Mathematical problems in theoretical biology, (Stakgold, I.; Joseph, D. D.; Sattinger, D. H., Nonlinear Problems in the Physical Sciences and Biology. Nonlinear Problems in the Physical Sciences and Biology, Springer Lecture Notes in Mathematics, No. 324 (1973), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0266.92002
[13] Prigogine, I.; Glansdorff, P., Structure, stabilité et fluctuations (1971), Masson: Masson Paris · Zbl 0246.73005
[14] Rabinowitz, P. H., A global theorem for nonlinear eigenvalues: problems and applications, (Zarantonello, E. H., Contribution to Nonlinear Functional Analysis (1971), Academic Press: Academic Press London/New York) · Zbl 0212.16504
[15] Sattinger, D. H., Topics in Stability and Bifurcation, (Springer Lecture Notes in Mathematics No. 309 (1972), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0448.35011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.