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472 Ben Abda et al.4. Applications4.1. The Robin inverse problemLet u the solution of the problem⎧⎨ ∆u = 0, in Ω∂u⎩∂n = g, on Γ c∂u∂n + ϕu = 0 on Γ iThe inverse Robin problem is to find a function ϕ such that the solution of the previousproblem satisfies u = f, on M, where M is a part of accessible boundary Γ c ; for theexistence and uniqueness of the solution see [3, 4, 6, 7]. In this work we suppose thatM = Γ c , our objective is to approach the function ψ on Γ i . The field we simulate is givenby u(x, y) = f 2 (x, y) = exp(10y) ∗ sin(10x) + exp(3y) cos(3x) + 10(y 3 − 3yx 2 ), thenwe use both of the algorithm to approach u and ∂u∂n , respectively, on Γ i. We give in thefigure 3 the approximation of ϕ for a = b = 5, 10 and 15 and we take for the degree ofthe polynomial of approximation n = 5, 8 and 10 respectively.(11)241012500−1−20−2−4−5−3−6−10−4−8−5−10−15−60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−120 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 3. Curves of ϕ with u = f 1 and its approximation for a = b = 5, 10 and a = b = 15and n = 5, 8, 104.2. Cracks problemIn this section, we give an algorithm to determine cracks lying on a priori knowninternal line. We want to identify the crack on Γ c = Ω 1 ∩Ω 2 by considering the followingCauchy problem⎧⎪ ⎨⎪ ⎩∆u = 0, in Ω \ σu = f, on Γ c∂u∂n = g, on Γ cu = 0 on σWhere Ω and Γ c are defined in section 3; σ is a set in Γ c . For numerical tests we considerthe function f 3 = (r) 1/2 cos( θ 2), the crack is on the x-axis and is specified by the partwhere f has a jump, it coincides with σ = [0, 0.5]. By using the algorithm defined insection 2 we can complete the solution of (1) − (2) with f = f 3 and φ = ∂f3∂n on Γ c.(12)TAMTAM –Tunis– 2005
Cauchy problem for Laplace’s equation 473We take for the degree of our polynomials of approximation n = 10, 12 and n = 14 seefigure 4.0.80.80.80.70.70.70.60.60.60.50.50.50.40.40.40.30.30.30.20.20.20.10.10.1000−0.10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 4. Curves of the function u = f 3 and its approximation for n = 10, 12 and 14, on Γ i5. References[1] D. D. ANG, N. H. NAGHIA AND N. C. TAM, “Regularized solutions of a Cauchy problem forthe Laplace equation in an irregular layer a three-dimensional model.”, Acta Math. Vietnam,1998, 23, pp. 65-74.[2] V. Y. ARSENIN AND A. N. TIKHONOV, “Solutions of Ill-posed Problems.”, Winston and Sons,Washington, 1997.[3] A. BEN ABDA, H. D. BUI, “Planar crack identification for the transient heat equation.”, J.Inverse Ill-Posed Probl. 11, 2003, no. 1, 27–31.[4] S. CHAABANE, M. JAOUA, “Identification of Robin coefficient by the means of boundarymeasurements.”, Inverse Problems, 15, 1999, pp. 1425-1438.[5] J. CHENG, Y. C HON, T. WEI AND M. YAMAMOTO, “ Numerical computation of a Cauchyproblem for Laplace’s equation.”, ZAMM. Z. Angew. Math. Mech, 2000, pp. 1-16.[6] D. FASINO, G. INGLESE, “An inverse Robin problem for Laplace’s equation, theoretical resultsand numerical methods.”, Inverse Problems 15, 1999, pp. 41-48.[7] G. INGLESE, “An inverse problem in corrosion detection.”, Inverse Problems 13, 1997, pp.977-994.[8] DE MOTTONI AND G TALENTI, “Stabilisation and error bound for the inverse Laplace transform.”,Numer. Func. Anal. Optimiz, 1981.[9] H. J. REINHARDT, H. HAN AND D. N. HÀO, “Stability and regularization of a discrete approximationto the Cauchy problem for Laplace equation.”, SIAM J. Numer. Anal 36, 1999, pp.890-905.[10] G. TALENTI, “Recovering a function from a finite number of moments.”, Inverse Problems3, 1987, pp. 501-517.TAMTAM –Tunis– 2005
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PréfaceOrganiser la seconde éditi
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Comité d’organisationMohamed Abd
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SOMMAIRE / CONTENTSI Conférences I
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Equilibre dans un système dynamiqu
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Arlequin method: Practical impacts
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Application de la méthode de Gauss
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Conférences InvitéesInvited Prese
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4 Amara et al.1. IntroductionWe are
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6 Amara et al.2.2. The nonlinear Na
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8 Amara et al.4. Numerical resultsW
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10 Auger et al.1. Introduction :Dan
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12 Auger et al.La condition de stab
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14 Auger et al.3.1. Taux de migrati
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16 Auger et al.L’équilibre rapid
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18 Auger et al.[7] BRAVO DE LA PARR
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Quelques aspects mathématiques etn
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22 El Alaoui Talibi M.- Modèle d
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24 El Alaoui Talibi M.[3] M. Chamba
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26 Habbal1. IntroductionAngiogenesi
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28 HabbalThe pressure drop denoted
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30 Habbaltheorem 1 There exists a N
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32 HabbalFigure 2. Second Nash loop
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34 Hauray et al.1. IntroductionWe a
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36 Hauray et al.minimal time interv
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38 Hauray et al.From this last theo
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Approximation de l’opérateur d
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42 LemrabetLorsque δ → 0, l’é
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44 Lemrabetavec[∆ ∗ (δ)c = [I
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46 Lemrabet6. Bibliographie[1] N. B
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48 Jaafar-Belaid et al.1. Introduct
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50 Jaafar-Belaid et al.where f(ρ)
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52 Jaafar-Belaid et al.202040406060
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IIContrôleControl55
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58 Arfaoui1. IntroductionCe travail
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60 ArfaouiLe système adjoint assoc
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62 Arfaoui[3] H. ARFAOUI , « Comma
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64 Benzekri et al.1. Global control
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66 Benzekri et al.ẏ = ∂H∂x =
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0 1 2 3 4 5 668 Benzekri et al.32.5
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70 Akian et al.1. IntroductionWe co
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72 Akian et al.We prove that v t+δ
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.74 Akian et al.0.0−1.0Exact solu
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76 Bokanowski et al.1. General fram
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78 Bokanowski et al.One interesting
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80 Bokanowski et al.4. Numerical ex
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Sur les problèmes de contrôle opt
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84 Metouileur lorsque u est dans L
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86 MetouiThéorème 2 Soit ū ε le
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88 Metoui[5] L.S. HOU, S.S. RAVINDR
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Système d’information intégré
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Gestion et modélisation des ressou
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Random perturbations of reduced gra
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Global Optimization of Water Resour
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Global Optimization of Water Resour
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IVEquations DifférentiellesDiffere
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114 B. Abdelkader1. IntroductionTel
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116 B. AbdelkaderNotons que les con
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118 B. AbdelkaderAlors pour tout X
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120 Bouzahir1. IntroductionWe consi
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122 Bouzahirwhere the linear operat
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Goursat boundary value problem forh
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126 A. Guezane-Lakoud et al.3. Func
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128 A. Guezane-Lakoud et al.5. Exis
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ACP neuronale : application à l’
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132 Chitroubl’approximation de la
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134 Chitroubcompression égal à 3.
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136 Chitroub[4] J. P. Nougier, Mét
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138 Ferchichi et al.1. Introduction
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140 Ferchichi et al.soit T −1 = (
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142 Ferchichi et al.[4] G.I. BISCHI
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144 Hafidi1. IntroductionOn étudie
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146 Hafidia ) ∫ Ωpdx → +∞ qu
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148 HafidiLEMME 3.2. On a lim R(θ
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150 Lefebvre1. IntroductionSoit (X
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152 LefebvreOn peut aussi écrire q
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154 Lefebvre5. BibliographieD.R. Co
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156 Meskine1. IntroductionDans le p
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158 Meskinefaibles σ( ∏ L M ,
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160 Meskine[12] E. YA. KHRUSLOV, L.
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162 K. Saoudi1. IntroductionL’ét
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164 K. Saoudice qui montre que la s
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166 K. Saoudieton aboutit au résul
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168 K. Saoudietc 1 + c 2 = 1 ∫(u
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170 K. SaoudiRemarque 3.1. Du lemme
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172 K. Saoudiet∫v(t, x) dxΩest c
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VEstimation d’ErreursError Estima
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178 Achchab et al.1. IntroductionDu
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180 Achchab et al.such that}Xh 2 ={
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182 Achchab et al.[2] B.ACHCHAB, M.
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184 Alla et al.1. IntroductionLes e
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186 Alla et al.3. Position du probl
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IsoValue-0.00070533-0.000604452-0.0
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190 Achchab et al.1. IntroductionLe
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192 Achchab et al.où T hi/2 est le
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IsoValue0.000933570.002800710.00840
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196 El Dabaghi et al.1. Motivation
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198 El Dabaghi et al.0 ≤ λ i ≤
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200 El Dabaghi et al.Figure 4. Mail
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Residual error estimators for the t
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204 Kharrat et al.The step (3) need
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206 Kharrat et al.following estimat
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VIMécanique des FluidesFluid Mecha
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212 Abdelwahed et al.1. Introductio
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214 Abdelwahed et al.Ainsi, suivre
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216 Abdelwahed et al.Figure 3. Isov
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Procédure spectrale avec diagonali
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220 El Guarmah et al.où Ra et P r
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222 El Guarmah et al.M 10 20 25 35
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Simulation de l’onde de crue via
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226 El Dabaghi et al.de R 2 , de fr
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228 El Dabaghi et al.INRIA-MODULEFm
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INRIA-MODULEF230 El Dabaghi et al.I
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232 Amoura et al.1. IntroductionFor
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234 Amoura et al.where u = rot r ψ
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236 Amoura et al.CURRENT FUNCTION5
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238 Frih et al.1. IntroductionLa mo
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240 Frih et al.et dans la fracture,
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242 Frih et al.6. Bibliographie[1]
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244 Hasnaoui et al.1. IntroductionL
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246 Hasnaoui et al.On obtient alors
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248 Hasnaoui et al.5. Conclusion et
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250 Hernane-Boukari1. IntroductionW
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252 Hernane-Boukarianda 3 =−11 +
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254 Kloucha et al.1. Motivation et
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256 Kloucha et al.Si le domaine Λ
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INRIA-MODULEF0INRIA-MODULEF.250INRI
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Dimensions fractales : attracteurs
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262 Lamrini Uahabi et al.4. Attract
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264 Lamrini Uahabi et al.l 0 = λ
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266 Lamrini Uahabi et al.En conséq
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Numerical analysis for the problem
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270 El-Kyal et al.d(u) = 1 2(∇u +
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272 El-Kyal et al.Theorem 3.1 There
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274 Marchand et al.1. IntroductionD
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276 Marchand et al.On remarque en p
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278 Marchand et al.dans la formulat
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280 Mezali et al.1. Motivation et m
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282 Mezali et al.s’annulant sur c
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284 Mezali et al.Temps CPUTemps Ela
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R. Touihri & S. Ghnimi *Méthode de
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288 Touihri et al.Les équations go
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290 Touihri et al.Tol N It (Newt) t
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292 Touihri et al.5. Bibliographie[
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Décomposition de domaine pour un m
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DDM pour les fractures 297et−→
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DDM pour les fractures 299dont l’
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Arlequin method: Practical impacts
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Arlequin method 303of the Arlequin
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Arlequin method 3052.2. Penalized A
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Arlequin method 307refinements of t
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Reduction methods and uncertaintypr
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Reduction methods and uncertainty p
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Reduction methods and uncertainty p
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0.00e+00 1.00e−11 2.00e−11 3.00
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Homogénéisation d’un problème
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Problème de conduction-rayonnement
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Problème de conduction-rayonnement
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Equation d’Hamilton-Jacobi 3231.
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Equation d’Hamilton-Jacobi 325qui
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0Equation d’Hamilton-Jacobi 3272
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Détermination du nombre de région
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Simulation des courants de Foucault
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Une méthode d’accélération de
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Schéma SRNHS 3491. IntroductionUn
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Schéma SRNHS 3513. Application du
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Schéma SRNHS 3535. ConclusionLes r
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Smoothing and compressing surfaces
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Problème de convection en milieu p
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0
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Condensation de masse pour la méth
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Condensation de masse 367montre que
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Condensation de masse 369Le terme h
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Condensation de masse 371Aet Qile f
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VIIIModèles CinétiquesKinetic Mod
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376 Ben Abdallah et al.1. Introduct
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378 Ben Abdallah et al.where B ∓
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380 Ben Abdallah et al.ture that th
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382 Degond et al.1. IntroductionOn
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384 Degond et al.q φ s (x, t)/(|q|
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386 Degond et al.Enfin l’opérate
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Les métaheuristiques : application
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Les métaheuristiques 391simulé fu
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Les métaheuristiques 393Fig. 1 Dia
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Les métaheuristiques 395Fig.4 : R
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Prices after capacity addition in m
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Multi-user elastic demand communica
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Shape optimization 4051. Introducti
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Shape optimization 4072.1. Variatio
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Shape optimization 409(a)(b)(c)(d)F
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Problèmes d’optimisation en éco
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Assimilation de données pour l’e
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Page 443 and 444: Écart à la Réciprocité et ident
Page 445 and 446: Identification de fissures planes 4
Page 451 and 452: Algorithme de Kohn et Vogelius 4331
Page 453 and 454: Algorithme de Kohn et Vogelius 435l
Page 455 and 456: Algorithme de Kohn et Vogelius 4375
Page 457 and 458: Résolution d’un problème de Cau
Page 463 and 464: Problème inverse géométrique 445
Page 469 and 470: Identification de fissures 4511. In
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Page 473 and 474: Application de l’algorithme deNeu
Page 475 and 476: Complétion de données en élastic
Page 477 and 478: Complétion de données en élastic
Page 479 and 480: Analytic extensions on an annulus:a
Page 481 and 482: Analytic extensions on an annulus 4
Page 483 and 484: Analytic extensions on an annulus 4
Page 485 and 486: −1 −0.8 −0.6 −0.4 −0.2 0
Page 487 and 488: Cauchy problem for Laplace’s equa
Page 489: Cauchy problem for Laplace’s equa
Page 495 and 496: Modélisation asymptotique des onde
Page 497 and 498: Ondes de relief 479 uuuv 1 1 pu v
Page 499 and 500: Ondes de relief 481( )ˆeiZw( C e D
Page 501 and 502: Ondes de relief 4836. Bibliographie
Page 503 and 504: Régularisation pour l’aéroacous
Page 509 and 510: Miroir à retournement temporel 491
Page 515 and 516: Vibro-acoustique instationnaire 497
Page 517 and 518: Vibro-acoustique instationnaire 499
Page 519 and 520: Ondes dans les milieux poroélastiq
Page 525 and 526: The implicitly restarted Arnoldi me
Page 527 and 528: ¨§¨ §IRAM method 509To overcome
Page 529 and 530: IRAM method 511The application of t
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Page 534 and 535: 516 Achchab1. IntroductionDans la m
Page 536 and 537: 518 AchchabNous montrons dans le pa
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522 Derbel et al.1. IntroductionLa
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524 Derbel et al.On se propose de d
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A Stochastic partial differential e
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528 El Saadidiffusion process to a
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530 El Saadiwhere δ Xi(t) is the D
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532 El Saadi5. References[1] A. L.
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534 Ben Miled et al.1. Introduction
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536 Ben Miled et al.nature de l’e
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538 Ben Miled et al.Ensuite on étu
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Optimal spatial distribution of a b
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542 Mchich et al.at time t. The com
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544 Mchich et al.3∑where r = r i
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XIIIStructureStructure547
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550 Ayadi1. IntroductionConsider a
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552 AyadiFor all 0 ≤ p ≤ i, P p
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554 AyadiFigure 3. The curves above
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Analyse mathématique et numérique
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558 Chamekh et al.2. Modèle de tig
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560 Chamekh et al.Γ sr(s)r(σ)Figu
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Modélisation de l’effet dynamiqu
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564 RahmaniI 2 étant l’identité
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566 Rahmani• ( u 1δ1∫+ ,0u 1δ
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Résolution d’un systéme d’ela
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570 Saidoù u vérifie :n∑n∑j=1
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572 SaidEn effet :∣ u(y, s) 1+α
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Régularisation d’un problème d
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576 Achchab et al.On définit : F +
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578 Achchab et al.3. Estimation a p
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Modélisation d’un pieuR. Aboulai
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582 Aboulaich et al.Figure 1. Struc
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584 Aboulaich et al.5. Résultats n
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XIVThéorie des GraphesGraph Theory
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590 Hlaoui1. IntroductionMore and m
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592 Hlaoui3. The New Graph Represen
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594 Hlaoui1 1 2 3 4 1 1 3 411 421 4
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596 M. Nekri et al.1. IntroductionL
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598 M. Nekri et al.proposés. Ces m
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600 M. Nekri et al.cycle de longueu
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TAMTAM -Tunis- 2005 602
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El Guarmah, M., 218El Kacimi, A., 2
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