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

• Published in: Nonlinear analysis Vol. 135; pp. 158 - 193
• Main Authors: Eisner, Jan, Väth, Martin
• Format: Journal Article
• Language: English
• 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

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...