Critical points for reaction-diffusion system with one and two unilateral conditions

Jan Eisner; Jan Žilavý

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 2, page 173-180
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Eisner, Jan, and Žilavý, Jan. "Critical points for reaction-diffusion system with one and two unilateral conditions." Archivum Mathematicum 059.2 (2023): 173-180. <http://eudml.org/doc/298972>.

@article{Eisner2023,
abstract = {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.},
author = {Eisner, Jan, Žilavý, Jan},
journal = {Archivum Mathematicum},
keywords = {reaction-diffusion system; critical points; unilateral conditions},
language = {eng},
number = {2},
pages = {173-180},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Critical points for reaction-diffusion system with one and two unilateral conditions},
url = {http://eudml.org/doc/298972},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Eisner, Jan
AU - Žilavý, Jan
TI - Critical points for reaction-diffusion system with one and two unilateral conditions
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 2
SP - 173
EP - 180
AB - 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.
LA - eng
KW - reaction-diffusion system; critical points; unilateral conditions
UR - http://eudml.org/doc/298972
ER -

References

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  1. Eisner, J., Kučera, M., Väth, M., Global bifurcation of a reaction-diffusion system with inclusions, J. Anal. Appl. 28 (4) (2009), 373–409. (2009) MR2550696
  2. Eisner, J., Väth, M., Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas, Nonlinear Anal. 135 (2016), 158–193. (2016) MR3473115
  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). (2015) 
  4. Kučera, M., Väth, M., 10.1016/j.jde.2011.10.016, J. Differential Equations 252 (2012), 2951–2982. (2012) MR2871789DOI10.1016/j.jde.2011.10.016
  5. Mimura, M., Nishiura, Y., Yamaguti, M., 10.1111/j.1749-6632.1979.tb29492.x, Ann. N.Y. Acad. Sci. 316 (1979), 490–510. (1979) Zbl0437.92027DOI10.1111/j.1749-6632.1979.tb29492.x
  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). (2018) 
  7. Turing, A.M., 10.1098/rstb.1952.0012, Philos. Trans. Roy. Soc. London Ser. B 237 (641) (1952), 37–72. (1952) DOI10.1098/rstb.1952.0012

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