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

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...

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Bibliographic Details
Published inNonlinear analysis Vol. 135; pp. 158 - 193
Main Authors Eisner, Jan, Väth, Martin
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2016
Subjects
Bifurcations
Global bifurcation
Hyperbolas
Instability
Mapping
Multivalued map
Neumann boundary condition
Nonlinearity
Obstacles
Reaction–diffusion system
Signorini condition
Stability
Stationary solution
Topological degree
Turing instability
Unilateral obstacle
Variational inequality
secondary
Multivalued map
Unilateral obstacle
Turing instability
Variational inequality
Signorini condition
Neumann boundary condition
Reaction–diffusion system
Stationary solution
Topological degree
Global bifurcation
primary
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2016.01.006