| Title:
|
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples (English) |
| Author:
|
Eisner, Jan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
119-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
bifurcation |
| Keyword:
|
spatial patterns |
| Keyword:
|
reaction-diffusion system |
| Keyword:
|
mollification |
| Keyword:
|
inclusions |
| Keyword:
|
semipermeable membranes |
| Keyword:
|
unilateral inner sources |
| MSC:
|
35B32 |
| MSC:
|
35J85 |
| MSC:
|
35K40 |
| MSC:
|
35K57 |
| MSC:
|
35K58 |
| MSC:
|
47H04 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0977.35020 |
| idMR:
|
MR1826476 |
| DOI:
|
10.21136/MB.2001.133929 |
| . |
| Date available:
|
2009-09-24T21:48:04Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133929 |
| . |
| Reference:
|
[1] J. Eisner: Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.Math. Bohem. 125 (2000), 385–420. MR 1802290 |
| Reference:
|
[2] J. Eisner, M. Kučera: Spatial patterns for reaction-diffusion systems with conditions described by inclusions.Appl. Math. 42 (1997), 421–449. MR 1475051, 10.1023/A:1022203129542 |
| Reference:
|
[3] D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order.Springer, Berlin, 1983. MR 0737190 |
| Reference:
|
[4] V. G. Maz’ya, S. V. Poborchi: Differentiable Functions on Bad Domains.World Scientific, Singapore, 1997. MR 1643072 |
| Reference:
|
[5] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha, 1967. MR 0227584 |
| Reference:
|
[6] R. E. Showalter: Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations.Mathematical Surveys and Monographs, AMS, Providence, RI, 1997. MR 1422252 |
| . |
