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SUMMARY:A macroscopic limit for an ecology model. - Gaël Raoul (Ecole pol
 ytechnique)
DTSTART:20170517T130000Z
DTEND:20170517T140000Z
UID:TALK72304@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:We are interested in PDE models that are used in evolutionary 
 ecology to investigate the effect of climate change on species' range. Mor
 e precisely\, we will consider the Spatial Infinitesimal Model\, a Kinetic
  model\, and the Kirkpatrick-Barton model\, a macroscopic model. Our goal 
 will be to provide a rigorous macroscopic limit between those two models. 
 We will also detail a biological study of the effect of pollen dispersion\
 , where the macroscopic limit mentioned is used.\n\nTo describe the macros
 copic limit from the Spatial Infinitesimal Model to the Kirkpatrick-Barton
  model\, we take advantage of a Tanaka inequality satisfied by the reprodu
 ction operator\, combined to parabolic estimates to control the spatial dy
 namics of the solution. As a by-product of this argument\, we obtain estim
 ates on a higher moment of solutions of the kinetic model\, provided the r
 eproduction rate is large enough.
LOCATION:MR4\, Centre for Mathematical Sciences
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