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UID:6322@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210928T100000
DTEND;TZID=Europe/Paris:20210928T120000
DTSTAMP:20241209T162631Z
URL:https://www.i2m.univ-amu.fr/evenements/spatial-dynamics-of-some-reacti
 on-diffusion-models-in-heterogeneous-media/
SUMMARY:Mingmin Zhang (I2M\, Aix-Marseille Université): Spatial Dynamics o
 f Some Reaction-Diffusion Models in Heterogeneous Media
DESCRIPTION:Mingmin Zhang: The talk will be in English.\nTitle:  Spatial 
 Dynamics of Some Reaction-Diffusion Models in Heterogeneous Media\nSupervi
 sor: Prof. François Hamel\nCo-supervisor: Prof. Xing Liang\n[su_spacer s
 ize="10"]\nJury members:\n\n\n\nGuillemette Chapuisat\nAix-Marseille Unive
 rsité\n\n\nArnaud Ducrot   (rapporteur)\nUniversité Le Havre Normandie
 \n\n\nFrancois Hamel (supervisor)\nAix-Marseille Université\n\n\nXing Lia
 ng    (co-supervisor)\nUniversity of Science and Technology of China\n\n
 \nYuan Lou\nOhio State University &amp\; Shanghai Jiao Tong University\n\n
 \nPhilippe Souplet\nUniversité Sorbonne Paris Nord\n\n\nXuefeng Wang   
 (rapporteur)\nThe Chinese University of Hong Kong-Shenzhen\n\n\nYaping Wu\
 nCapital Normal University\, China\n\n\n\nAbstract: We first study the eff
 ect of the geometry of the underlying domain on propagation phenomena of b
 istable equations. We consider bistable equations in funnel-shaped domains
  of \\mathbb{R}^N made up of straight parts and conical parts with positiv
 e opening angles. We investigate the large time dynamics of entire solutio
 ns emanating from a planar front in the straight part of such a domain and
  moving into the conical part. We show a dichotomy between blocking and sp
 reading. We also show that any spreading solution is a transition front ha
 ving a global mean speed\, which is the unique speed of planar fronts\, an
 d that it converges at large time in the conical part of the domain to a w
 ell-formed front whose position is approximated by expanding spheres. More
 over\, we provide sufficient conditions on the size R of the straight part
  of the domain and on the opening angle $\\alpha$ of the conical part\, un
 der which the solution emanating from a planar front is blocked or spreads
  completely in the conical part. We finally show the openness of the set o
 f parameters $(R\,\\alpha)$ for which the propagation is complete. Then\, 
 we consider a one-dimensional patchy model made up of a succession of reac
 tion-diffusion equations in homogeneous media\, where novel interface matc
 hing conditions are introduced to reflect the movement behavior of individ
 uals when they come to the edge of a patch. Firstly\, we consider this mod
 el in a spatially periodic environment. We  establish the well-posedness 
 rigorously for the Cauchy problem. We then investigate the spreading prope
 rties  and the existence of pulsating traveling waves in the positive and
  negative directions. Secondly\, we study a simplified two patchy model in
  \\mathbb{R} which consists of two homogeneous habitats. Our interest is t
 o investigate propagation dynamics  of solutions to the Cauchy problem wi
 th compactly supported initial data in different reaction combinations. We
  first derive the spreading properties of solutions in the KPP-KPP case. T
 hen\, in the KPP-bistable framework we investigate different conditions un
 der which  the solutions of the Cauchy problem may show different dynamic
 s in the bistable patch\, that is\, blocking\, virtual blocking or propaga
 tion. In particular\, when propagation occurs\, a global stability result 
 is proved. The results in the KPP-bistable frame can also be extended to t
 he bistable-bistable setting with certain hypotheses.\nhttps://orcid.org/0
 000-0002-2051-5402
CATEGORIES:Soutenance de thèse,Analyse Appliquée
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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