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Bifurcation and non-equilibrium phase transitions in a chemical reaction with diffusion

  • A. M. Albano
  • N. B. Abraham
  • D. E. Chyba
  • Mario Martelli
Conferenze
  • 23 Downloads

Summary

Under suitable assumptions the dynamics of a class of chemical reactions with diffusion is governed by a parabolic partial differential equation with a cubic non-linearity and Neumann boundary conditions. Stationary and homogeneous solutions, stationary but non-homogeneous solutions as well as time and space dependent solutions are possible. By tuning the characteristic parameters of the system we can modify the domain of attraction of the system's equilibria and the way they are reached from different initial conditions. We can also explain the processes of nucleation and hysteresis.

Keywords

Wave Front Neumann Boundary Condition Travel Wave Solution Strong Maximum Principle Parabolic Partial Differential Equation 
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.

Sunto

Lo studio di una classe di reazioni chimiche porta, sotto ipotesi opportune, ad un'equazione differenziale alle derivate parziali di tipo parabolico nella concentrazione ϱ (x, t), con un termine cubico in ϱ e condizioni ai limiti del tipo di Neumann. Sono possibili soluzioni omogenee e stazionarie, soluzioni stazionarie ma non omogenee e soluzioni dove ϱ dipende sia dalla posizione che dal tempo. Si esamina la stabilità e il dominio di attrazione degli stati di equilibrio del sistema, il mondo in cui sono raggiunti a partire da condizioni iniziali assegnate nonchè i processi di isteresi e di catalizzazione.

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References

  1. [A-W]Aronson D. G. andWeinberger H. F., Springer-Verlag Lecture Notes,446, 5–50 (1975).MathSciNetGoogle Scholar
  2. [B-M]Bedeaux D. andMazur P., Physica,1 A A, 1 (1981).MathSciNetGoogle Scholar
  3. [F]Fife P. C.,Mathematical Aspects of Reacting and Diffusing Systems. (Springer-Verlag, Berlin, 1970).Google Scholar
  4. [R]Rabinowitz P.,J. of Functional Analysis.7, 487–513 (1971).CrossRefMathSciNetMATHGoogle Scholar
  5. [S]Schlögl F., Z. Phys.,253, 147 (1972).CrossRefGoogle Scholar

Copyright information

© Birkhäuser-Verlag 1982

Authors and Affiliations

  • A. M. Albano
    • 1
    • 2
    • 3
  • N. B. Abraham
    • 1
    • 2
    • 3
  • D. E. Chyba
    • 1
    • 2
    • 3
  • Mario Martelli
    • 1
    • 2
    • 3
  1. 1.Physics DepartmentBryn Mawr CollegeBryn MawrUSA
  2. 2.Mathematics DepartmentBryn Mawr CollegeUSA
  3. 3.Università CalabriaArcavacata di RendeCosenzaItaly

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