Article
MSC:
35B32,
35J85,
35K40,
35K57,
35K58,
47H04,
47N20 | MR 1826476 | Zbl 0977.35020 | DOI: 10.21136/MB.2001.133929
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
bifurcation; spatial patterns; reaction-diffusion system; mollification; inclusions; semipermeable membranes; unilateral inner sources
bifurcation; spatial patterns; reaction-diffusion system; mollification; inclusions; semipermeable membranes; unilateral inner sources
Summary:
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.
Related articles:
References:
[1] J. Eisner: Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions. Math. Bohem. 125 (2000), 385–420. MR 1802290
[2] J. Eisner, M. Kučera: Spatial patterns for reaction-diffusion systems with conditions described by inclusions. Appl. Math. 42 (1997), 421–449. DOI 10.1023/A:1022203129542 | MR 1475051
[3] D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order. Springer, Berlin, 1983. MR 0737190
[4] V. G. Maz’ya, S. V. Poborchi: Differentiable Functions on Bad Domains. World Scientific, Singapore, 1997. MR 1643072
[5] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha, 1967. MR 0227584
[6] R. E. Showalter: Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations. Mathematical Surveys and Monographs, AMS, Providence, RI, 1997. MR 1422252
Search
Partner of
