Hopf bifurcation in quasilinear reaction-diffusion systems

  • Herbert Amann
Research Articles
Part of the Lecture Notes in Mathematics book series (LNM, volume 1475)


Periodic Orbit Hopf Bifurcation Analytic Semigroup Compact Resolvent Bessel Potential Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amann, H. (1986): Quasilinear Evolution Equations and Parabolic Systems. Trans. Amer. Math. Soc. 29, 191–227MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Amann, H. (1988): Dynamic Theory of Quasilinear Parabolic Equations—I. Abstract Evolution Equations. Nonlinear Analysis, T M & A. 12, 895–919MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Amann, H. (1990): Dynamic Theory of Quasilinear Parabolic Equations-I. Reaction-Diffusion Systems. Diff.-Integral Eq. 3, 13–75MathSciNetzbMATHGoogle Scholar
  4. 4.
    Amann, H. (1990): Ordinary Differential Equations. An Introduction to Nonlinear Analysis, de Gruyter, BerlinGoogle Scholar
  5. 5.
    Crandall, M.G., Rabinowitz, P.H. (1977/8): The Hopf Bifurcation Theorem in Infinite Dimensions. Arch. Rat. Mech. Anal. 67, 53–72MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    de Groot, S.R., Mazur, P. (1962): Non-Equilibrium Thermodynamics. North Holland, AmsterdamzbMATHGoogle Scholar
  7. 7.
    Drangeid, A.K. (1989): The Principle of Linearized Stability for Quasilinear Parabolic Evolution Equations. Nonlinear Analysis, T M &, A 13, 1091–1113MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Fife, P. (1979): Mathematical Aspects of Reacting and Diffusing Systems. Lecture Notes in Biomath. No. 28, Springer Verlag, Berlin-Heidelberg-New YorkzbMATHGoogle Scholar
  9. 9.
    Henry, D. (1981): Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. No. 849, Berlin-Heidelberg-New YorkGoogle Scholar
  10. 10.
    Pazy, A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Operators. Springer Verlag, Berlin-Heidelberg-New YorkCrossRefzbMATHGoogle Scholar
  11. 11.
    Da Prato, G., Lunardi, A. (1986): Hopf Bifurcation for Fully Nonlinear Equations in Banach Spaces. Ann. Inst. Henri Poincaré-Analyse non Linéaire. 3, 315–329zbMATHGoogle Scholar
  12. 12.
    Da Prato, G., Lunardi, A. (1988): Stability, Instability and Center Manifold Theorem for Fully Nonlinear Autonomous Parabolic Equations in Banach Spaces. Arch. Rat. Mech. Anal. 101, 115–141CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Herbert Amann

There are no affiliations available

Personalised recommendations