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SUMMARY:CAA Talk: Some optimisation problems in spatial ecology (Mazar
 i\, Paris-Sorbonne Université)
UID:96a4e103-6fec-4ae3-9ae1-77244f717c40
DESCRIPTION:Some optimisation problems in spatial ecology Idriss Mazar
 i (Laboratoire Jacques-Louis Lions\, Paris-Sorbonne Université) Abstr
 act: In this talk\, we will present some optimisation problems arising
  in spatial ecology. In a broad way\, the main question of this talk i
 s: how can we spread resources in an optimal manner? Assuming our popu
 lation can be modeled via the Fisher-KPP equation $$-muDelta u-u(m-u)=
 0$$ with Neumann or Dirichlet boundary conditions\, and with a resourc
 es distribution $m:Omega to mathbb R$\, we investigate two questions: 
 1) Under natural ($L^1$ and $L^infty$) constraints on the resources di
 stribution $m$\, which resources distribution yields the optimal chanc
 e of survival? Can we take into account more precise models involving 
 a drift? These questions can be recast as spectral optimisation proble
 ms and lead to concentration properties. 2) Under the same $L^1$ and $
 L^infty$ constraints on $m$\, which resources distribution yields the 
 maximal population size? Here\, we prove the existence of bang-bang (i
 .e characteristic functions) maximisers for large enough diffusivities
  and investigate several qualitative properties. A new asymptotic meth
 od to obtain the existence result is introduced. An unexpected qualita
 tive result is the influence of the diffusivity on the optimisers\, wh
 ich opens up many questions about fragmentation properties for such mo
 dels and optimisation problems. https://en.www.math.fau.de/applied-ana
 lysis/caa-talks/
DTSTART:20200218T104500Z
DTEND:20200218T114500Z
LOCATION:03.323 Besprechungsraum
DTSTAMP:20260723T200845Z
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