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Concentration of solutions for some singularly perturbed Neumann problems. (English) Zbl 1184.35024
Gursky, Matthew J. (ed.) et al., Geometric analysis and PDEs. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, June 11–16, 2007. Berlin: Springer; Florence: Fondazione C.I.M.E. (ISBN 978-3-642-01673-8/pbk; 978-3-642-01674-5/ebook). Lecture Notes in Mathematics 1977, 63-115 (2009).
The author studies some techniques for constructing solutions to a class of singularly perturbed problems with a precise asymptotic behavior. One of the main motivations for the study of these equations arises from reaction-diffusion systems, concerning in particular the so-called Turing instability.
For the entire collection see [Zbl 1166.35001].
Reviewer: Jiaqi Mo (Wuhu)

MSC:
35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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