The Lifshitz-Slyozov equation in biology
Erwan Hingant (Université de Picardie Jules Verne)
Thursday 16th May 14:00-15:00 Maths 311B
Abstract
The Lifshitz-Slyozov (LS) equation is a transport equation with a nonlocal field describing the growth of clusters in size by addition and depletion of their elementary unit. This equation takes its origins in the theory of phase transition where precipitation of grains in a supersaturated solution yields a new (solid) phase. The eponymous author of the equation proposed a kinetic approximation of this phenomenon which becomes widely used in a variety of biological contexts (fibrin formation, actin filaments, amyloid formation, adipocyte, etc). In this
presentation, we will provide an overview of the theory of the LS equation and its development together with some applications arising in biology, along with a presentation of some results (existence, uniqueness, long-time behaviour) of a variant with nucleation implemented as a boundary condition to the transport equation.
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