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Stability and instability of equilibria on singular domains. (English) Zbl 1180.35106

Mucha, Piotr Bogusław (ed.) et al., Nonlocal and abstract parabolic equations and their applications. Based on the conference, Bȩdlewo, Poland, 2007. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-05-8/pbk). Banach Center Publications 86, 103-113 (2009).
Summary: We show existence of nonconstant stable equilibria for the Neumann reaction-diffusion problem on domains with fractures inside. We also show that the stability properties of all hyperbolic equilibria remain unchanged under domain perturbation in a quite general sense, covered by the theory of Mosco convergence.
For the entire collection see [Zbl 1166.00016].

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35B41 Attractors
35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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