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Seminario Dottorato: Singular limits of reaction-diffusion equations and propagation of interfaces

Wednesday 15 February 2012 - Cecilia De Zan

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 22 February 2012 h. 15:00, room 2BC30
Cecilia De Zan (Padova, Dip. Mat.)
"Singular limits of reaction-diffusion equations and propagation of interfaces"

-Abstract
Interfacial phenomena are commonplace in physics, chemistry, biology. They occur, for example, whenever a continuum that can exists in at least two different chemical or physical "states" is present, and there is some mechanism that generates or enforces a spatial separation between these states. The separation boundary is called an interface. In mathematics, interfaces appear in the study of the asymptotic limits of evolving systems, like reaction-diffusion equations.
After a simple introduction about the connections between reaction-diffusion equations and the wavefronts they generates, we present some mathematical approaches to the study of evolving interfaces. We present the classical level set-approach and a geometrical approach introduced by Barles and Souganidis in 1998. Then we show how this second approach can be applied in the study of the asymptotic limits of reaction-diffusion equations. Finally we show a simple generalization we obtained for nonlinear and possibly degenerate diffusions.

Rif. int. C. Marastoni, T. Vargiolu

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