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This book is the outcome of a conference held at the Centro De
Giorgi of the Scuola Normale of Pisa in September 2012. The aim of
the conference was to discuss recent results on nonlinear partial
differential equations, and more specifically geometric evolutions
and reaction-diffusion equations. Particular attention was paid to
self-similar solutions, such as solitons and travelling waves,
asymptotic behaviour, formation of singularities and qualitative
properties of solutions. These problems arise in many models from
Physics, Biology, Image Processing and Applied Mathematics in
general, and have attracted a lot of attention in recent years.
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