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UID:7193@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210928T100000
DTEND;TZID=Europe/Paris:20210928T120000
DTSTAMP:20220516T125709Z
URL:https://www.i2m.univ-amu.fr/events/spatial-dynamics-of-some-reaction-d
iffusion-models-in-heterogeneous-media/
SUMMARY:Spatial Dynamics of Some Reaction-Diffusion Models in Heterogeneous
Media - Mingmin Zhang
DESCRIPTION:SOUTENANCE DE THÈSE\n\n\nThe talk will be in English.\n\n\n[su
_spacer size="10"]\nTitle: Spatial Dynamics of Some Reaction-Diffusion
Models in Heterogeneous Media\n[su_spacer size="10"]\nSupervisor: Prof. F
rançois Hamel\nCo-supervisor: Prof. Xing Liang\n[su_spacer size="10"]\n\n
\n\nJury members:\n\n\n\n\n\n\n\nGuillemette Chapuisat\nAix-Marseille Univ
ersité\n\n\nArnaud Ducrot (rapporteur)\nUniversité Le Havre Normandi
e\n\n\nFrancois Hamel (supervisor)\nAix-Marseille Université\n\n\nXing Li
ang (co-supervisor)\nUniversity of Science and Technology of China\n\
n\nYuan Lou\nOhio State University &\; 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 W
u\nCapital Normal University\, China\n\n\n\n[su_spacer size="10"]\n\n\nAbs
tract: We first study the effect of the geometry of the underlying domain
on propagation phenomena of bistable equations. We consider bistable equat
ions in funnel-shaped domains of \\mathbb{R}^N made up of straight parts a
nd conical parts with positive opening angles. We investigate the large ti
me dynamics of entire solutions emanating from a planar front in the strai
ght part of such a domain and moving into the conical part. We show a dich
otomy between blocking and spreading. We also show that any spreading solu
tion is a transition front having a global mean speed\, which is the uniqu
e speed of planar fronts\, and that it converges at large time in the coni
cal part of the domain to a well-formed front whose position is approximat
ed by expanding spheres. Moreover\, we provide sufficient conditions on th
e size R of the straight part of the domain and on the opening angle $\\al
pha$ of the conical part\, under which the solution emanating from a plana
r front is blocked or spreads completely in the conical part. We finally s
how the openness of the set of parameters $(R\,\\alpha)$ for which the pro
pagation is complete. Then\, we consider a one-dimensional patchy model ma
de up of a succession of reaction-diffusion equations in homogeneous media
\, where novel interface matching conditions are introduced to reflect the
movement behavior of individuals when they come to the edge of a patch. F
irstly\, we consider this model in a spatially periodic environment. We
establish the well-posedness rigorously for the Cauchy problem. We then in
vestigate the spreading properties and the existence of pulsating travel
ing waves in the positive and negative directions. Secondly\, we study a s
implified two patchy model in \\mathbb{R} which consists of two homogeneou
s habitats. Our interest is to investigate propagation dynamics of solut
ions to the Cauchy problem with compactly supported initial data in differ
ent reaction combinations. We first derive the spreading properties of sol
utions in the KPP-KPP case. Then\, in the KPP-bistable framework we invest
igate different conditions under which the solutions of the Cauchy probl
em may show different dynamics in the bistable patch\, that is\, blocking\
, virtual blocking or propagation. In particular\, when propagation occurs
\, a global stability result is proved. The results in the KPP-bistable fr
ame can also be extended to the bistable-bistable setting with certain hyp
otheses.\n[su_spacer size="10"]\nZoom: https://univ-amu-fr.zoom.us/j/95091
925651?pwd=am0ySTlJc3BJdGE0b1E4bDdkVUMxZz09\n\n\nMeeting ID: 950 9192 5651
\nPassword: see mail\n[su_spacer size="10"]\n\n\nhttps://orcid.org/0000-00
02-2051-5402\n\n[su_spacer size="10"]
CATEGORIES:Hybrid,Soutenance de Thèse
LOCATION:FRUMAM\, St Charles (2ème étage)\, 3 Place Victor Hugo\, Marseil
le\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=FRUMAM\, St Charles (2èm
e étage):geo:0,0
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