Abstract
Finite-time singularities occurring in mathematical models of free-surface flows indicate that important qualitative changes are taking place; for problems in solid and fluid mechanics this includes topological transitions—blow-up and pinch-off. For many problems, the dynamics leading to the formation of such singularities are described by self-similar solutions of the governing nonlinear partial differential equations. We present an analytical and numerical study of these similarity solutions and discuss their stability.
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Witelski, T.P. (2002). Computing finite-time singularities in interfacial flows. In: Bourlioux, A., Gander, M.J., Sabidussi, G. (eds) Modern Methods in Scientific Computing and Applications. NATO Science Series, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0510-4_12
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