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

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• 作者：Jan Eisner^a ; ^{jeisner@prf.jcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Martin Vä ; th^b ; ^{martin@mvath.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 35B32 ; 35K57 ; secondary ; 35J60 ; 35J88 ; 47H04 ; 47H11 ; 47J20
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：135
• 期：Complete
• 页码：158-193
• 全文大小：808 K

文摘

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.