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• W1559930110 abstract "This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and where typical scales of the solution shrink to zero as the singularity is approached. Upon a similarity transformation, exact self-similar behaviour is mapped to the fixed point of a {it infinite dimensional dynamical system} representing the original dynamics. We show that the dynamics close to the fixed point is a useful way classifying the structure of the singularity. Specifically, we consider various types of stable and unstable fixed points, centre-manifold dynamics, limit cycles, and chaotic dynamics." @default.
• W1559930110 created "2016-06-24" @default.
• W1559930110 creator A5001806960 @default.
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• W1559930110 date "2007-11-03" @default.
• W1559930110 modified "2023-09-27" @default.
• W1559930110 title "A catalogue of singularities" @default.
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