Description : This video illustrates the study by E. Bernard, M. Doumic and P. Gabriel https://hal.archives-ouvertes.fr/hal-01363549/document by showing the time behaviour of the solution to the following growth-fragmentation equation:
$$\frac{\partial}{\partial t} u(t,x) + \frac{\partial}{\partial t} (x u(t,x)) + B(x)u(t,x)=4B(2x)u(t,2x),\qquad u(0,x)=u^{in}(x).$$
The numerical scheme is explicit, and uses a splitting between the transport operator and the fragmentation operator, on a geometric grid.
This allows to capture the asymptotic periodic behaviour (due to a lack of dissipativity in the equation).
https://hal.inria.fr/medihal-01407826
Contributor : Marie Doumic
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Submitted on : Friday, December 2, 2016 - 3:36:13 PM
Last modification on : Sunday, March 31, 2019 - 1:24:43 AM
