Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas

0458505 - MÚ 2017 RIV GB eng J - Journal Article
Eisner, J. - Väth, Martin
Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 135, April (2016), s. 158-193. ISSN 0362-546X. E-ISSN 1873-5215
Institutional support: RVO:67985840
Keywords : reaction-diffusion system * turing instability * global bifurcation
Subject RIV: BA - General Mathematics
Impact factor: 1.192, year: 2016
http://www.sciencedirect.com/science/article/pii/S0362546X16000146

For a reaction–diffusion system which is subject to Turing’s diffusion-driven instability and which is equipped with unilateral obstacles of various types, the nonexistence of bifurcation of stationary solutions near certain critical parameter values is proved. The result implies assertions about a related mapping degree which in turn implies for “small” obstacles the existence of a new branch of bifurcation points (spatial patterns) induced by the obstacle.
Permanent Link: http://hdl.handle.net/11104/0258773