Saddle connections in parabolic differential equations

Authors

  • C. Miguel Blázquez Universidad Técnica Federico Santa María.
  • Elías Tuma Universidad Técnica Federico Santa María.

DOI:

https://doi.org/10.22199/S07160917.1994.0001.00005

Keywords:

Parabolicas, Funciones, Ecuaciones diferenciales parabólicas

Abstract

We assume the existence of a saddle connection between two hyperbolic equilibrium points. Necessary and sufficient conditzons are given for the existence of a connection for the perturbed equations. These connections are obtained from the zeros of a finite number of bifurcation functions.

Author Biographies

C. Miguel Blázquez, Universidad Técnica Federico Santa María.

Departamento de Matemática.

Elías Tuma, Universidad Técnica Federico Santa María.

Departamento de Matemática.

References

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[6] A. Friedman Hold, Rinehart and Winston 1969. Partial differential equation.

[7] J. K. Hale, X. B. Lin Heteroclinic orbit for retarded functional differential equation LCDS Report 8439 Brown University 1984

[8] .J. K. Hale Introduction to dynamic bifurcation. Lecture Notes in Mathematies. Springer Verlag, 1057 (1984).

[9] D. Henry Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, Springer Verlag, 840 (1981).

[10] X. B. Liu Exponential dichotomies and homoclinic orbit in retarded Functional Differential Equations LCDS Report 8439 Brown University. may 1984.

[11] A. Pazy Semigroups of linear operators and applications to partial differential equations Appl. Math. Se.. 44, Springer Verlag ( 1983)

[12] L. P. Sil'nikov 119 On the generation of a periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type. Math. USSR Sbornik, Mat. Sbornik Tom 77 vol 6(1968), 119.

Published

2018-04-03

How to Cite

[1]
C. M. Blázquez and E. Tuma, “Saddle connections in parabolic differential equations”, Proyecciones (Antofagasta, On line), vol. 13, no. 1, pp. 25-34, Apr. 2018.

Issue

Section

Artículos