1Numero d'ordre

Pascal Noble

Description

1Numero d'ordre : 48-2009 UNIVERSITE CLAUDE BERNARD (LYON 1) HABILITATION A DIRIGER DES RECHERCHES specialite : Mathematiques Appliquees Soutenue publiquement le 4 Decembre 2009 par Pascal NOBLE Titre : ANALYSE D'ECOULEMENTS EN EAUX PEU PROFONDES ET STABILITE DE SOLUTIONS PERIODIQUES POUR LES EQUATIONS DE SAINT VENANT ET DES SYSTEMES HAMILTONIENS DISCRETS devant le jury compose de Sylvie BENZONI Constantine M. DAFERMOS Mariana HARAGUS-LARGER David LANNES Jean-Michel ROQUEJOFFRE Jean-Claude SAUT Denis SERRE Jean-Paul VILA apres avis favorables de Constantine M. DAFERMOS Mariana HARAGUS-LARGER David LANNES

• modeles de saint venant


• justification rigoureuse


• roll waves


• stabilite de solutions periodiques pour les equations de saint venant et des systemes


• systemes hamiltoniens


• continuation des solutions periodiques

Sujets

• Jordan
• Lannes
• Constantine Dafermos
• Benzoni

Informations

• Publié par: profil-urra-2012
• Publié le: 01 décembre 2009
• Nombre de lectures: 16

Extrait

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ξ :n
μ :
F :n
(I−μF )n
η r rn
F , μn
(X )i,n 0≤i≤n
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N N lim n cov(X ,X ) = 00 n→+∞ 0,n r,nr=N
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d
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{y} {v} {φ}t t≥0 t t≥0 t t≥0
{θ} dt t≥0
θ =θ +wt+1 t t+1
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ˆθt
Tˆ ˆ ˆθ =θ +μL (y −φ θ ).t+1 t t t tt
μ Lt
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˜ ˆ ˜θ = θ −θ θt t t t+1
u v w˜ ˜ ˜ ˜θ = θ +μθ +θ ,t t t t
u T u u˜ ˜ ˜ ˜θ = (I−μLφ )θ , θ =θ =−θ ,t 0 0t+1 t t 0
v T v v˜ ˜ ˜θ = (I−μLφ )θ +Lv, θ = 0,t t tt+1 t t 0
w T w w˜ ˜ ˜θ = (I−μLφ )θ −w , θ = 0.t t+1t+1 t t 0
u˜{θ }t
v˜{θ }t
w˜{v} {θ } {w}t tt+1
v w˜ ˜θ θt
δ = (I−μF )δ +ξ, δ = 0t+1 t t t 0
tX
= Φ(t,s)ξs
s=0
{F} {ξ} (d×1)t t≥0 t t≥0
Φ(t,s)

(I−μF )(I−μF )···(I−μF ), t>s t t−1 s+1
I, t =s

0,
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TF =Lφt t t
ξ =Lv ξ =−w .t t t t t+1
¯ ¯F =E(F ) Z =F −F (I−μF )t t t t t t
¯I−μF = (I−μF )+μZ.t t t
(0) (0) (0)¯J = (I−μF )J +ξ, J = 0t tt+1 t 0
(0) (0) (0) (0)¯H = (I−μF )H +μZJ , H = 0t tt+1 t t 0
(0) (0)
δ = J +H .t t t
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δt
(0) (1) (n) (n)
δ =J +J +···+J +H ,t t t t t
(r) (n)
J , 0≤r≤n Ht t
(0) (0) (0)¯J = (I−μF )J +ξ ; J = 0t tt+1 t 0
(r) (r) (r−1) (r)¯J = (I−μF )J +μZJ ; J = 0, 0≤t<rt tt+1 t t t
(n) (n) (n) (n)
H = (I−μF )H +μZJ ; J = 0, 0≤t<nt tt+1 t t t
q≥ 1 X ={X } (l×1)n n≥0
δ = (δ(r)) Xr∈N
(δ,q) C ={C ,···,C }1 q
1≤m<s≤q m t ,···,t (s−m) t ,···,t t ≤···≤1 m m+1 s 1
t <t +r≤t ≤···≤tm m m+1 s
sup |Cov(X ···X ,X ···X )|≤C δ(r)t ,i t ,i t ,i t ,i s1 1 m m m+1 m+1 s s
i ,···,i1 s
X i Xn,i n
p ≥ 1 n ∈ N G = {G} (d×d)t t≥0
(δ,p(n+2))
X
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r
D (G) j ∈ {1,···,n} 0 ≤p,n
s≤t<∞
X j/2G ···G ≤D (G)(t−s) . i i p,n1 j
pn/j
s≤i <···<i ≤t1 j
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