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Unilateral sources and sinks of an activator in reaction-diffusion systems exhibiting diffusion-driven instability
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SYSNO ASEP 0504264 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Unilateral sources and sinks of an activator in reaction-diffusion systems exhibiting diffusion-driven instability Author(s) Fencl, M. (CZ)
Kučera, Milan (MU-W) RID, SAI, ORCIDSource Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 187, October (2019), s. 71-92Number of pages 22 s. Language eng - English Country GB - United Kingdom Keywords maximal eigenvalue ; positively homogeneous operators ; reaction–diffusion systems ; unilateral terms ; Turing's patterns Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000476707200004 EID SCOPUS 85064321149 DOI 10.1016/j.na.2019.04.001 Annotation A reaction–diffusion system exhibiting Turing's diffusion driven instability is considered. The equation for an activator is supplemented by unilateral terms of the type s − (x)u − , s + (x)u + describing sources and sinks active only if the concentration decreases below and increases above, respectively, the value of the basic spatially constant solution which is shifted to zero. We show that the domain of diffusion parameters in which spatially non-homogeneous stationary solutions can bifurcate from that constant solution is smaller than in the classical case without unilateral terms. It is a dual information to previous results stating that analogous terms in the equation for an inhibitor imply the existence of bifurcation points even in diffusion parameters for which bifurcation is excluded without unilateral sources. The case of mixed (Dirichlet–Neumann) boundary conditions as well as that of pure Neumann conditions is described. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2020 Electronic address http://dx.doi.org/10.1016/j.na.2019.04.001
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