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SUMMARY:Enrique Zuazua: Reaction-diffusion models\, constraints and contro
 l
DTSTART;VALUE=DATE-TIME:20190415T130000Z
DTEND;VALUE=DATE-TIME:20190415T140000Z
DTSTAMP;VALUE=DATE-TIME:20261015T135042Z
UID:indico-event-42@cern.ch
DESCRIPTION:Enrique ZUAZUA\n\nDeustoTech-Bilbao & UAM-Madrid  & LJLL-Pari
 s\n \nReaction-diffusion models\, constraints and control\n \n \nAbstra
 ct:\nReaction-diffusion equations are ubiquitous in a variety of fields in
 cluding combustion and population dynamics.\nThere is an extensive mathema
 tical literature addressing the analysis of steady state solutions\, trave
 ling waves\, and their stability\, among other properties.\nControl proble
 ms arise in many applications involving these models and\, often times\, c
 ontrol and/or state constraints emerge as intrinsic requirements of the pr
 ocesses under consideration.\nThere is also a broad literature on the cont
 rol of those systems\, addressing\, in particular\, issues such as the pos
 sibility of driving the system to a given final configuration in finite ti
 me. But\, the necessity of preserving the natural constraints of the proce
 ss are rarely taken into account.\nIn this lecture we shall present the re
 cent work of our team on the Fisher-KPP and Allen-Cahn or bistable model\,
  showing results of two different types. First\, the fact that constrained
  controllability for large enough time can be achieved. And\, second\, as 
 a consequence\, in particular\, of the classical comparison principle for 
 parabolic problems\, negative results showing the existence of threshold e
 ffects so that some targets can never be achieved\, or the existence of a 
 waiting time for them to be reached.  This is in sharp contrast with the 
 unconstrained case where parabolic systems can be controlled in an arbitra
 rily small time.\nThis presentation is based on joint work with Jérôme L
 ohéac (CNRS-Nancy)\, Camille Pouchol and Emmanuel Trélat (LJLL-Sorbonne 
 Univ.)\, Dario Pighin (UAM-Madrid)\, and Giuseppe Floridia (Univ. Napoli).
 \n\nhttps://indico.unina.it/event/42/
LOCATION:Sala riunioni I livello\, Dipartimento di Matematica e Applicazio
 ni "R. Caccioppoli"
URL:https://indico.unina.it/event/42/
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