| Title:
|
Critical points for reaction-diffusion system with one and two unilateral conditions (English) |
| Author:
|
Eisner, Jan |
| Author:
|
Žilavý, Jan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
173-180 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show the location of so called critical points, i.e., couples of diffusion coefficients for which a non-trivial solution of a linear reaction-diffusion system of activator-inhibitor type on an interval with Neumann boundary conditions and with additional non-linear unilateral condition at one or two points on the boundary and/or in the interior exists. Simultaneously, we show the profile of such solutions. (English) |
| Keyword:
|
reaction-diffusion system |
| Keyword:
|
critical points |
| Keyword:
|
unilateral conditions |
| MSC:
|
34B15 |
| MSC:
|
35B36 |
| MSC:
|
92C15 |
| idZBL:
|
Zbl 07675587 |
| idMR:
|
MR4563029 |
| DOI:
|
10.5817/AM2023-2-173 |
| . |
| Date available:
|
2023-02-22T14:42:11Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151564 |
| . |
| Reference:
|
[1] Eisner, J., Kučera, M., Väth, M.: Global bifurcation of a reaction-diffusion system with inclusions.J. Anal. Appl. 28 (4) (2009), 373–409. MR 2550696 |
| Reference:
|
[2] Eisner, J., Väth, M.: Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas.Nonlinear Anal. 135 (2016), 158–193. MR 3473115 |
| Reference:
|
[3] Kouba, P.: Existence of nontrivial solutions for reaction-diffusion systems of activator-inhibitor type with dependence on parameter.Master's thesis, Č. Budějovice, Faculty of Science, University of South Bohemia, 2015, (in Czech). |
| Reference:
|
[4] Kučera, M., Väth, M.: Bifurcation for reaction-diffusion systems with unilateral and Neumann boundary conditions.J. Differential Equations 252 (2012), 2951–2982. MR 2871789, 10.1016/j.jde.2011.10.016 |
| Reference:
|
[5] Mimura, M., Nishiura, Y., Yamaguti, M.: Some diffusive prey and predator systems and their bifurcation problems.Ann. N.Y. Acad. Sci. 316 (1979), 490–510. Zbl 0437.92027, 10.1111/j.1749-6632.1979.tb29492.x |
| Reference:
|
[6] Pšenicová, M.: Newton boundary value problem for reaction-diffusion system of activator-inhibitor type with parameter.Bachelor thesis, Č. Budějovice (2018), Faculty of Science, University of South Bohemia, 2018, (in Czech). |
| Reference:
|
[7] Turing, A.M.: The chemical basis of morphogenesis.Philos. Trans. Roy. Soc. London Ser. B 237 (641) (1952), 37–72. 10.1098/rstb.1952.0012 |
| . |
