Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples

Jan Eisner

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 119-140
  • ISSN: 0862-7959

Abstract

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The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.

How to cite

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Eisner, Jan. "Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples." Mathematica Bohemica 126.1 (2001): 119-140. <http://eudml.org/doc/248825>.

@article{Eisner2001,
abstract = {The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.},
author = {Eisner, Jan},
journal = {Mathematica Bohemica},
keywords = {bifurcation; spatial patterns; reaction-diffusion system; mollification; inclusions; spatial patterns; semipermeable membranes; mollification; inclusions; unilateral inner sources},
language = {eng},
number = {1},
pages = {119-140},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples},
url = {http://eudml.org/doc/248825},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Eisner, Jan
TI - Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 119
EP - 140
AB - The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.
LA - eng
KW - bifurcation; spatial patterns; reaction-diffusion system; mollification; inclusions; spatial patterns; semipermeable membranes; mollification; inclusions; unilateral inner sources
UR - http://eudml.org/doc/248825
ER -

References

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  1. Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions, Math. Bohem. 125 (2000), 385–420. (2000) MR1802290
  2. Spatial patterns for reaction-diffusion systems with conditions described by inclusions, Appl. Math. 42 (1997), 421–449. (1997) MR1475051
  3. Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983. (1983) MR0737190
  4. Differentiable Functions on Bad Domains, World Scientific, Singapore, 1997. (1997) MR1643072
  5. Les méthodes directes en théorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  6. Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs, AMS, Providence, RI, 1997. (1997) MR1422252

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