Spatial patterns for reaction-diffusion systems with conditions described by inclusions

Jan Eisner; Milan Kučera

Applications of Mathematics (1997)

  • Volume: 42, Issue: 6, page 421-449
  • ISSN: 0862-7940

Abstract

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We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.

How to cite

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Eisner, Jan, and Kučera, Milan. "Spatial patterns for reaction-diffusion systems with conditions described by inclusions." Applications of Mathematics 42.6 (1997): 421-449. <http://eudml.org/doc/32991>.

@article{Eisner1997,
abstract = {We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.},
author = {Eisner, Jan, Kučera, Milan},
journal = {Applications of Mathematics},
keywords = {reaction-diffusion systems; variational inequalities; inclusions; bifurcation; stationary solutions; spatial patterns; destabilizing effect; variational inequalities inclusions; stationary solutions},
language = {eng},
number = {6},
pages = {421-449},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spatial patterns for reaction-diffusion systems with conditions described by inclusions},
url = {http://eudml.org/doc/32991},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Eisner, Jan
AU - Kučera, Milan
TI - Spatial patterns for reaction-diffusion systems with conditions described by inclusions
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 6
SP - 421
EP - 449
AB - We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
LA - eng
KW - reaction-diffusion systems; variational inequalities; inclusions; bifurcation; stationary solutions; spatial patterns; destabilizing effect; variational inequalities inclusions; stationary solutions
UR - http://eudml.org/doc/32991
ER -

References

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