Study of the Quasi-Static Norton-Hoff Heat Problem
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Study of the Quasi-Static Norton-Hoff Heat Problem Jamel Ferchichi — Jean-Paul Zolésio. N° 4432 Mars 2002. ISSN 0249-6399. ISRN INRIA/RR--4432--FR+ENG. THÈME 4. apport de recherche.
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(263) A¤ AosbBg ¢ Z#h^¨hZKg£^_g djV%wqZZlqdjZKi%l Z ¢ Zh^_g ¢ p h^¨G^_g% b i¤we^_fhwe^EZlzdj^_Ykb>djZKl«ac^_g%¿>Z n defdjV¤ZhZKacfrs^¨d¬p & lefha_`¤de^cfhgfB®deV%Z¥8fhwqdefhgG§¦8fB©Z6`Fbmdj^_fhg£bBg n defdeV%ZkdeZYi0Zwjbmdj`%wqZ#lefBac`¤de^cfBg£fBªdeV%Z#V¤Z<b>dfhg%Z> Z#bBaclqfh^¨hZkdjV%ZPZ<bB¿ sfhgde^cg6`%^¨d¬p f> deV%ZZ,urdeZg n Z n YkbBi¤i%^cg¤ ^_gdjV%ZlqZsKfhg n lqdeZi° c¬g©deV%ZdjV¤^cw n fhg%ZPZ n Zwe^¨hZdeV%Zlqdewefhg¤ sKfhgdj^_g6`%^_d¬pdeV%wefh`¤hVdWdjV%ZosfBg6de^cg6`%^¨d¬p+fBdjV%Z n ^_lelq^ciFbmdj^_fhgYZsbBg%^_sVFbBai0fPZwK mKdU µ)< H ,5 ¹ ,5 KK95# ¤ µ ZoVFb<hZodjV%Z fha_acfT'^_g%Zlzdj^_YbmdjZlK % µ @ 1
(264) +." Y<; 0 ; HI-/V; 0 E 0 ! ;B HI 0 V 0 ) & <; 0 ;[-/D B 0 K-/ -M) 5. ,-- +.- 1 D< 0 . & / ) 8 - 32! 4 A ) 8 .t 0 4 A ) 8 - 1 0 +\!EB;J-M) 0 = 1 -/CE Q 0 K-/'(! 1 EDD P N ¹°¹ '¹ % µ . . H. i Gi. . . . @ *1. d8^_l'Z<bBlzpdjf n Zwq^_BZ r^cbdeV%Z ®q bB`%sVp]GsVªbBwqd 4^_g%Z6`Fb>ac^¨d¬p ¼ A
(265) lqZZ c. A ) .7 - & ) .7 -. 587 3 D % '& D F !. $. ZKaclqZ"vfh^_g%s<bBwqZ lL^_g%ZKr`%bBac^¨d¬p A
(266) lqZZ0BA;ªi%wqfTG^ n ZKl. 324 &. deV%Zg YfhwqZfThZKw. . ! A 324. & . . & )8 . % R. !A. . . -. . . . . . ) 8 . ! A 354. . - %. R . ) 8 . -. . . ^cl'sKfhgdj^_gr`¤fh`%lea¨pZY ¢ Z n%n ^_g%^_g Q -<¼ ^¨dW fha_acfT'l & / ) 8 - 35! 4 A ) 8 b>g n deV%Zoi%wefrfB^_lLb>sV%^_BZ n. lq^cg¤sZ. Q. ¯Ll8bsKfhg%lqZ6`%Zg¤sZ ¼ fhg%Zos<b>gZbBle^_a_p n Z n `¤sZodjVFb>d % µ @ 7 587 $ !/& $ BDB % !'& $ ! A ) 8 -. E!J;[-QED ;[-. u ) -. !A. A. ) 8 . -. . . 0 *^-/+ 0 -/j.
(267) A \.
(268)
(269) ! #" #$%&!
(270) '(&)*!+," #-.0/. % µ
(271) +. Y<; 0 ; HI-/V; 0 E 0 ! ;BHI 0 V 0 ) 7 <; 0 h;[-/D B 0 K-/ -M) 0 h( 0 (A4BV 0 K-/ ?&0 h]_*8 0 ) 5 ! A ) - 0 Q
(272) ! ) - ? :9 R 7 / ) 8 ) .7 - I 8 / /
(273) / 8 E! 0 - 5 ! A ) - 0 Q
(274) ! ) - ? :9 Rh 7 ) 8 / ) .7 - I 8 / /
(275) / 8 .t 0F0 I
(276) 1 0 +\!EB;G-M) 0 = 1 -/CEaQ 0 K-/'(! 1 EDD P 7 N µ ¹ º } µ µ R ¹ ¶ Z n Zg¤fBdjZ '&
(277) 7 /&
(278) 7 . ? 3 3 . g n ZKw i%weZ,r^cfh`¤l acZKYYb A¤ deV%ZªlqZ6`%Zg¤sZ /& @ ^_l ¢ fB`%g n Z n ^cg"deV%Z®wqZKFZ²u¤^¨ ®bBgFb>sV lqiFbBsKZ ! b>g n deV6`%l@fhg¤ZPsbBg"Z²uGdewjbBs,d b'le` ¢ leZKr`¤Z g%sK Z /& @ 'V%^_sV«sKfhghZwqhZl9ªZbB¿6a_p ^_g ! > ± Z,d & 1 djV%^_l@PZ<bB¿ac^_Y^_d ¼ bBg n bBlqle`%YZ /& @ ^¨djleZKa_}sfBg6BZwqhZlxPZ<bB¿6a¨p"djfTªbBw n l & 1 % µ
(279) aCEIH 0 -/+ & 1 <; 0 ;[-/D B 0 K-/ -M) 3 ? Q-/+.I-/CE+ & 1 & N ¹°¹ '¹ % µ @ D. !.
(280) !A .
(281). U. 3. h<. -. S. $ -. . . . $ -. . r. 3 95 3. !. S. $ S -. -. $.
(282). 5. !. $. . !. BA . $. e. .. !. !. @ 6. H. $ S -. $. O. ^. . . !. !. . !. U. !. $. . $. /.. !. .. 20. $. 10. @ B6. i Gi. r] ^cg%sKZ
(283) ¥8fhwqdefhgG¬¦LfB^_l >bBwe^cb>dj^_fhgFb>a
(284) A^A Z> deV%Z4lefha_`¤dj^_fhg weZbBac^54Z©djV¤Z4Y^_g%^_Y"`%Y fBkdjV%Z b>lelefrs^cb>deZ n ]Eg¤Zwe>p ¼ ^_d8^_l8ZbBlqp#djfsV%Zs¿deV%Z fhaca_fT'^cg¤^_g%Z6`Fb>ac^¨d¬p ¼ fhw'bBgp % : 3 3 5 7 : D % !#H $ED F G 5 7 A H !#H $ % H ! 5 7 : D % !'& $ED F G 5 7 A & 'V¤ZweZ ^_lL bsKfhghZ,ubBg n¾ b>deZ<bB`Gu n ^_}ZwqZg dj^cb ¢ a_Z Yb>i%i%^_g%% ±Z,d(3 1 3 ¼ b>ssfBw n ^_g%ha¨pdeV%ZªlqZ6`%ZKg%sZ 3 sKfhghZwqhZlxlzdjwqfhg%ha¨podjfT®b>w n l(3 1 ^_g Q.- !#"%$ b>g n lqfkbBaclqf^_g Q0F !#" $ ^¨d'pr^cZKa n l 3 3 1 D !1H $ED F 5 7 A H % H ! A
(285) 5 7 D !/& $ED F 7 & 7 5 5 % G G . : : % deV%Zg 3 3 1 D !#H $ED F 5 7 A H % H ! 0 ! 5 7 A & $
(286) 5 7 D !/& $ED F 7 5 % G G . . : : % 'V¤^csV^cghfBa_BZl 3 3 1 D !#H $ED F 5 7 A H % H ! A ! 5 7 D !/& $ED F $ 7 & 7 5 5 % G G 1 . : : % 10. A \.
(287) > . 0". + #. . ^¨dLbBwe^_leZKlWdjVFb>d. 3 3 5 7 : D % !/& $ED F ! : $ S:9 F % !/& $ F ) 7.'V¤ZweZbBl'djV%ZoYkbBi%i%^_g% H G ; ! F $S:9 F % !#H $ ) 7.- ^_lWªZbB¿6a_p+a_ les ¼ sfhghZ²ufhgdjf! > 587 3 D !'& $ D F < le^_g%sZ c¬g n ZZ n°¼ djV%Z `%g%s,dj^_fhg D % !'& $ D F ^cl'i0fhle^¨dj^¨hZ bBg n 0 & : % F . : 3 354324 : ! 7I5 : $ 'V%^ca_Z ; ! F $S:9 F % !'& $ ! F $S:9 F % !/& 1 $
(288) ^cg Q F !#"%$²¼ 'V¤Zg%sKZ `¤le^_g% ' b>defh` l'acZKYkYkb
(289) AlqZZ bBa_lef ¼ 587 3 : 1 D % !/& 1 $ D F 587 3 : D % !/& $ED F ^¨d' fha_acfT'l 5 7 3 : 1 D % !/& 1 $ D F G 5 7 A & 1 5 7 3 : 1 D % !#H $ED F G 5 7 A H 1 !1H/$ % H ! deV6`%l ¼ & 1 weZbBac5^ 4Z«deV%ZY^cg¤^cY`%Y fB 1 ¼°¢ p`¤g%^c6`%ZKg%Zlql & 1 &
(290) AlqZZbBa_le+ f A DbBg n lqf deV%ZoacZKYYb
(291) RG [ ª^_l'i%wefTBZ n 0. 0. mº U} µh< U}T ¹ 3 g r ¹ 3 9 5 3 5 ¶ Z ¢ ZKh^cg ¢ ph^¨r^cg%djV¤^clW `%g n bBYZgdbBa±a_ZYYkb¤ % µ @ f
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