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

Mathematica Bohemica (2001)

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

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topEisner, 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

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

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