Free Boundary Problemin Norton-Hoff Steady Flow with Thermal Effects
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Free Boundary Problem in Norton-Hoff Steady Flow with Thermal Effects Jamel Ferchichi — Jean-Paul Zolésio. N° 4417 Mars 2002. ISSN 0249-6399. ISRN INRIA/RR--4417--FR+ENG. THÈME 4. apport de recherche.
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(191) ' . "+$ V. ±m kj \$_qk_*¯@f$_wgJÅ¥ _¥ degeg_3demjp_*|k_wqjp_ s jkljp\$_ s de_w|u_wmjpdihK$degid¹j±t ¥ d¹jp\|k_*qko;_wx*j jkljp\$_ s ln^'hKdim)lK,jp\$_ o;_wmOhKgedeÇw_ s f$m$xjpdelnmOhKgJ¦[\²_ £ _wgelPx*dej±t ^`_*jk\$l s ¥ degigo$|ul £ d s _ jp\$_qk\$hKo_ s de_w|u_wmjpdihK$degid¹j±thKm s hKm)_zPo$|k_*qkqudilnm lK,jk\$_qk\OhKo;_ n|ph s di_*mjE¦ _ o;lndimj'lnf²j`jk\OhGj'lnf$| qjpf s t m$_w_ s q,lKm$getjpl`^`l £ _jk\$_·|k_*_;lnf$m s hK|ut 3 ¦ Ã ln|·jk\$_§lngigelZ¥ dim²$Å¥7_` ²z 0!dem hKm s h qko;_w_ s ª O_*g s dem ¦ ®_*j ;_wgelnm$nqjpl
(192) 1 quf$x\jk\OhGj ( G Q deqjp\$_hKquqklvxwdihGjp_ s ¤OlZ¥µ^ hGo$o$dem$'jkl :$ln| hKmt1 ] U. . (G. 8 _ . Q<G Q}M . (G. iQj i. QT . ( G Q<G 3 Q. . _ ] b Mv3 8 _. [\²_jk|phKm$quolK|ujp_ s o$|kln²gi_*^¸¥ digeg®mOhGjkf$|phKgeg¹t0_ s _ Om$_ s demjk|phKm²qko;ln|ujBqk_jpq. . . 8 _ G 8PQ}M 8 _ 4G 8 Q}M . . 8 _. NhKx\lKjp\$_*qk_qk_jpqBdim$\²_w|kd¹jpqBlKIhKgeg¿jp\$_o$|ulno;_w|ujkdi_*q,lG Å /hGm s P. G 8PQ . ¦. r = f}Á Z ¼  J Z²+?J G Á " ¼ [\$_0jp|phGm$qko;ln|ujlK,jk\$_0o$|uln$ge_w^ xwhKm m$lKj`;_ s lnm$_ ¥ d¹jp\²lnf²jBjp\$_jp|phGm$qko;ln|ujBlKIjp\$_ s hGjph²¦'U±mlKf$|,qudejkfOhGjkdilnm¿Å=jk\$_|kden\jy\OhGm s qud s _ diqBjp\$_lnm$g¹t s hGjhjpl,_Njp|khKm$qko;ln|jp_ s ¦ ³ |phGkjk\$_w|n_*m$_w|khKg¥¶hEt s l s _EhKg@¥ d¹jp\ jk\$deq1o$|uln$ge_w^deqjkl,x*lnm$qkd s _*| jk\OhGj,jp\$_ s k hGjhdeq·h JhG^'deg¹t g
(193) dem s _ zP_ s t¨hKgegjp\$_§h s ^`diquqkde$gi_ s lK^ hGdim$q quf$x\ jp\OhrjEÅ hrjgi_whKqujwÅ g ;_wgelnm$nq¶jkl 5 | G Q7ln|¶hKm.t *B¦ U±m(jk\$diqqu_wxjpdelnm°Å$ln| jk\$_·qph hK_·lKqkde^`o$gedix*dej±tKÅ ¥7_^ h hK_·jp\$_·lngegel¥ dem$ hKqkquf$^`o²jpdelnm°ÅO¥ \$dex\deqBh £ _w|t qkde^`o$gi_oOhK|jpdexwf$gihK| xEhGqk_K¦ 0w f + ? Á =HB C g C + FE+ 2 WJG M ]
(194) Q . . . @R.
(195) .
(196)
(197) ! "
(198) #$!%'&(") *+-,.,! "/ 01/ 243%567")8. [\@f$q`¥7_hK|u_ hK$ge_0jpl ln|k^ f$gihGjp_0jp\²_ jk|phKm²qko;ln|ujk_ s qujphGjpdex o$|kln²gi_*^¦ U 'j \OhKq'h qklKgif²jkdilKm GL6l8NM I;8PQ¶dem 8 8¦ BCC FHGsI G ORQS8SQT U#GL6R8Q;T WYXZU#Gs6l8Q [ @ 8 ] _ ` 8 dem 8 dem 8 a0bdcJe G ` 8PQ _ g ¬Z G ?@ QS8 D CCE dem 8 bdcJe GL6l8SQ _ h _ ` J G R j k ; I P 8 Q s G l 6 8. Q. U L G l 6 S 8 Q dem 8 a bdcJe ¥ d¹jp\ jp\²_;lnf$m s hK|ut(xwlnm s dejkdilnm²q BCCC 6l8 _ 6l5 lnm 35puv38 CC w I;8 _ h lnm 3 8 D y w x 8 ¬n G 2 Q8 C CCC z I;8 [ w I;8 _ lnm 35 a0{}| CE wyx 8 G ` 8 o x 8NMP~Y8SQ _ h lnm 3 8 _ B ; H67?>&+& 67H+ (6 . ;! I 3( ) P , + ZP 6?? C $ 43e6 , 3 + B;!. ¼ Ä$+ . . . . . . . & ,+& = & ,+.g VH+ 0. _ \Oh £ _jp\$_·lngegel¥ dem$`jp|khKm$qko;ln|j gi_*^'^'h " ¼ Æ B ; e + + >? V98 /mG Q (B+ . . bcJe G e Q _h % db cJe
(199) G. 8 e Q & 8 X . _h. f}¼ 0 OÂ ? ¼ = Ádc +I ¼ L Á f " ?J = ¼ G d Á f}Á 4?+? Á = B ;
(200) . /34+ FE a G M e M
(201) Q ;!=3 % 67 eC&;H+ h P 6= , k G e M
(202) Q + 5 | 0 & +&+& C =+ I 67?! Q3 + /A 98 4 67?!?! QP + (;! 3( 6 +V +V P 6 6 (R+ J I. !% &'( #QP " 6 I U$# % + 0 0 k w 8; GSG 8 e M Q 8 X . QT 8 0 _. ¬ .
(203) & . . . a. c k. c$k.
(204) T U#G e Q;T WYXZ U#G e Q G e 0 a )G 0 e QPQ . G
(205) T U#G e Q T W a g e Q bdcfe 0 a . g 0 e9a g 0 e. Á°Ádc ÁcQG Ádf}Á ? +? Á = ;!C [\²_jk|phKm$quolK|uj ge_w^`^'h Kh m s h§^`_w|u_x\$hKm$n_lK £ Gh |kdihK$ge_o²|kl £ d s _ : k G. ¬ 9 . . . . GPG. 8 e M
(206) Q'& 8 X . Q. _ c$k. _ c$k. .
(207) & 8 X . T U G 8 e & 8 X . QT W .
(208)
(209) T G 8 X . )G . & & . a g G e 8X . Q 8 e QPQT W a G g 8SQ e G Q. ¥ \²_w|k_GÅOln| hKmt0lno;_w|khGjpln| : G Q _ Z. G=[ .Q¦ [\²_wmÄjk\$_'|k_wquf$g¹j!deqqkf$o$o²gide_ s ÅIqkdem$xw_`jp\$_`^'hKo$o²dim$ a G 8 M X . G QPQydeq s de_w|u_wmPª jkd´hG$gi_dem h ¦ .
(210) G . Ádf}Á 4?+? Á G. =. .4&' T>? P ( T> 4& k _'&)(+* G e M FQ X G e. B CO >?. [dG 8PQ. . ;!!? / 3 % 6? eC&;. 8 r6. w 8N[dG 0 Q _ w 8 GSG . (;! E:6e3 Z;! E:+V DC ,98 4 67?!?! . k. M
(211) Q /mG 8SQ . k. . 6)/ 6 / . . . 8 .
(212). '& 8 X . Q;T 8 0. MF Q . 9;: =?< 0. G e M
(213) Q + 5 | B( A . /34+ FE k SG G ?8 e M
(214) Q 8 X . Q ;!& @ & , UI& 0 ! 0 > 0 G h M e M
(215) Q 0 ¼ Æ. " . 6 &+&. ¾ a ¼ ?7A$²+? Á = Ádf}Á 4?+? Á = B W !. G. B C. . '& . ? = !. C H+ Ke3% + ! IQPHA R ) 0 . /34+ FE. (+*. a. , , . 2. G M fp8NM
(216) 8SQ. ;!K3 % 67 eC&;+ h 0 ?0 +!K3( 6 +V +VH;! E:+V SC ,. #& 8 X . Q;T 8 0 _. w 8 2 GSGJIM Q. w 8 GJI. & 8 X . Q;T 8 0 [. w 8 , GSGJIM Q. & 8 X . Q;T 8 0. & 67 GJIM Q ;! !?!%%> Q3 !e3e3 &; U + !% &'$ QP A >? 6 67?!
(217) 43+ FE=>? 4 &;3 ! I U e3 % + 467C&;-. 0. Á°Ádc ÁcQf Ádf}Á ? +? Á = B )W cvdim$x*_jk\$_·f$m$xjpdelnmOhKg 2 G M f 8NM 8SQdeq nd £ _wmhKqlngegilZ¥ q : 2 G M fp8NM
(218) p8PQ _ G M?fp8Q [ , G M?fp8 M
(219) 8SQ jk\$_wm¿ÅOlnm0jp\$_·lnm²_\$hKm s Ų¥ d¹jp\ jp\²_MJhKx*jjk\OhGjjp\²_Mf$m$x*jkdilKm G M?fp8PQ deq¯@fOhKqud¹ª xwlnm £ _ z¥ dejk\ |u_wquo_*x*jjp@ l fp8 jp\$_*m5lnm jp\$_§lKjk\$_w|y\OhKm s , G M?f"M
(220) AQBdeq·xwlnm £ _ z@ª±xwlKm$xEh £ _'¥ dejk\5|k_wquo_*x*jjpl G)fp8NM
(221) 8SQ¦ U jBdeqB_*m$lnf$K\jkl'|u_*_*| jkl K ¦ G. . ¼ Æ. " . B W. 6 , G fM
(222) Q + . (*. ;!& @ & , UI& 0 ! 0 > 0 G h M f"M
(223) AQ0. . Z (B+ . / 34+ FE. . , , . 2. +& 8 X . M & 8 X . Q. G Mf. K.
(224) P.
(225)
(226) ! "
(227) #$!%'&(") *+-,.,! "/ 01/ 243%567")8. f}¼ 0OÂ ? ¼ = Ádc +I ¼ ( I ¼ = ? À a0 ¼ = ? +? Á = B -; G { M ^ Q _ G M . Q (BA J I. k.
(228) a G f Q Z _
(229) a. Ádf}Á 4?+? Á.
(230). G. =. P 6 &+& G M f Q + . G f Q Z. . . . X . ¼ Æ. B B. ]. 6 ,. . G Q . . G
(231) M f Q + . ?7b. I.
(232) & . [ c$kc$k T G
(233) a T O G fpQPQ< G O T a Q T Z b O b a k 8 X . a G f 8 X . Q Z ;! 3 % 67 )eC&;. & . G Q . l1 X X 1lX. XZ. 4G Q (. . X. . X. X. 1. &. k. & 8 X . a G)f,& 8 X . Q Z. . 4;: 6>< 0. 10. & +A @67?!
(234) ?> ZI. X ! M X !'& 5 5 !. A . /34+ FE. ¼ ¼ = @?J$*?"-? ½ÆÁdc +I ¼\GM¼ = "-? ¼  D = K+? Á = " ¼@Á ¼ B ;65 43( 6 !?! .4) 87 0 : ( + 4&'! 3ZP $ T> 4&. eC&; + . . 5| 5 5 5| 17X 1RX 1lX. 1yX. .
(235). ". ! % "$#
(236) ! ( )! ! )! " . + * , % L ! , M ,
(237) . 4G Q ]
(238) =X G M
(239) M f Q
(240). ;!& @ & , UI& 0 ! 0 > 0 G h M M f Q )9 !%? a. . . . /10324. " . . . . / 34+ FE a + h 0 0?+! ( 3 6 +V )+V;! E:+V D ! P &+&; & !. B B. 1 X
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