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$2 NO, $ )+*+ ( 2* $ 12< , #' *&*8* # $*2**2*

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7 @

7 @

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2

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- ; - < ; - ;

- ; - < ; - ;

α

α 7,!@

**2<$'Q*$'#'2*$*(*+(21**#+*)$62*9

6 6 6 2 2 6

= =

2 6 2 2 6 2

; - <- <

; (- <- < 7,@

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+()2,

*(4+$#(2$2**(2#7$'2$3$2(222<@92*

$#2)$

Z Z

Z Z

6 2

6

- -

- -

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7, @

*2

Z Z

Z

7 @

7 @

6 - -

- -

α αα α

= + + +

= + − +

7,H@

$*##'$*+()2

*2$ $P#+$(4(*2#+$ H I/ / /- - - - (+$ *(112(2*#

($$ 92#29+)$ $12<, /$$'#211+*$*# +()2 **2<$'

#2#2(([(2#$($)$2+#$#+()2

I

H

Z ZH I H

Z ZI H I

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= − + +

7,I@

)(+#$#$P1$Q9)+(+#/2

Z Z Z Z H I I H H I

Z Z Z Z H I H I I H

7 @

7 @

6 - - - -

- - - -

α α α αα α α α

= + + + + + + +

= + + + − + − +

7,E@

2$9(9#$+()2*

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/ / Z ZZ Z/ / 7 @ 7 @

$ $$ $

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- -

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− = +

7,@

Page 23: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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Z Z / /

Z Z/ / /

Z Z / /

Z Z/ / /

7 7 @ @

7 @

7 7 @ @

7 @

%$ $

$ $

$

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$ $ $

$ $

%$ $

$ $

$

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$ $ $

$ $

- -

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α

α

=

= = =

=

= = =

= +

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= + −

7,"@

,())"$'-/$+!$!'!/-0,

*#$2*30/**&*#$(*$2$P+<2,2*2/*

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+($9$#$29*22$,

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^ $<27 7 / @@

6>2∈

= = 7,F@

=2<,I&*8+

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#+#2#7,@/##(#4<$)$

/,

7= 7,G@

2(4$9*&)+*2*/112($(2+*)($*$2

a a/

9?7

η = 7, !@

2#*(#*4<$'#$28<++$#+)##*(#22**2$*

7#

*++*#$$2(*#+122*:)$2#(2$2*2+$2#**&*#

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# *++* *$11(+*:$#+2**2#+ $#2P4<$:

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! / /,,,/ $@ @ $ $ 5= ≠ ∈ 7, @

$(*+9

, 7 @/

9

5

! =

= 7, @

W*(*$#+!7Y6 A /@$*+2#*/*&*:$*/5*$

$2(2#2+#$259*$$2($*)*+(%<+#,

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* (#22* )+* # $$$< #$** #2*2+ $'2$ $

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* (#* #2 )2 * (#22* +(+* 7, @ 7, @, #+#2

#'($***#(#**&)##$2,

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#$11(#$2#2)*2$)2#7@,

'!"

H I

H I H

H I

! ! ! !

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− − − = −

7, H@

H I

I HI

H I

I H

! ! ! !

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! ! ! !

! ! ! !

− − − − =

− −

7, I@

H I E " F

I H E F "

H I " F E

" I H F " E

E " F H I

E F " I H

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! ! ! ! ! ! ! !

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! ! ! ! ! ! ! !

! ! ! ! ! ! ! !

− − − − − − − − − −

− − − = − − − − − − − − − − − −

7, E@

Page 26: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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F

H I E " F

I H E F "

H I " F E

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! ! ! ! ! ! ! !

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! ! ! ! ! ! ! !

! ! ! ! ! ! ! !

! ! ! ! ! ! ! !

− − − − − − − − − −

− − − − − − = − − − − − − − − −

− − −

7, @

*2#2(*#(*)#$#2<*$#$*+2**2,*

$2(*($+*7, I@7, @*#*(#*##*,$**($*7, H@

7, E@/$$2(*)$*($+#*$*21+2:(1+:7,G@,

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Z

Z

! !

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−=

7, "@

Z Z Z Z H I H I

Z Z Z ZH I H I H

Z Z Z ZH I H I

"

! ! ! ! ! ! ! !

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− − − − − − = − − − −

7, F@

Z ZZ H H

Z ZZ H H

H

Z Z Z ZH H

-

! !! !

! !! !

! ! ! ! ! ! ! ! ! !

= − − − + − − + +

7, G@

Z Z H

] Z ZH H

Z ZH

!

!

!

-

! ! !

! ! !

! ! !

= − − −

7,H!@

Page 27: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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Z Z Z Z H I H I

Z Z Z Z I H I H

I Z Z Z ZH I H I

Z Z Z ZI H I H

"

! ! ! ! ! ! ! !

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! ! ! ! ! ! ! !

− − − − − − − − = − − − −

7,H@

Z ZH H

Z ZH H

I Z Z Z ZH H

Z Z Z ZH H

-

! !! !

! !! !

! ! ! ! ! ! ! ! ! !

! ! ! ! ! ! ! ! ! !

− = − − + − − + + − − − − − − − +

7,H @

1$$9$**29*$2(*#(#*7,H@7,H @)$')/29$&$

*P#2*2*/)$*P#,2#7,H@*#a $*9(2

#7,H @*#HaI,

$2(#(#()')***$1

Z

/

B B B B

B

! !=

= + 7,HH@

WBB*#*$2(*#P$29#*++**(\!,

* ++* !B * (%<+* 1 )$2 #* / *&* 2*** # #$ :

$*,*(#22*#4<$2+2)*+**+92$*:

B B B B 7,HI@

B B B≠ 7,HE@

!

B B = 7,H@

Page 28: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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!

!

B B + = 7,H"@

*$***2#7,HH@))+*$+4###+(#$<#$*($#

<++$,

(*2#8 9 * $* * $* +()2 5 $* +2**2, *

*))** ($$ : +$2** *+(21 1+9(,$$2( # ($$ 9

** $#()#2*275/*@,

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7,HF@

W # #2*27'* ($$(+2* 2 $( * $**2 $2( # #2*2

77'*@,

$)$

/ /N /,,,/ O$ $ $ 5= 7,HG@

##2*275'@/*(112(2*#$$2(*5$*#+2**2$

# +()2 #+*2<+ )$ $ # $28 9 )2** +(2 ')**2 # *2<$ Q )$

(3(2**$1$2(2

$ $ $= + 7,I!@

7 @9

$ $ 7' σ= 7,I@

*++*/ #)P')2(2+*)$

7 / @N /,,,/ /,,,/ O$ * 7 5= 7,I @

7 / @N /,,,/ /,,,/ O$ * 5 *= 7,IH@

7 / @N /,,,/ /,,,/ O$ * 7 *= 7,II@

$<24#$'2#$2*$(92222*$+29##+(2*21(2

#**&*Q***#*$*#+()2#$*($*W*))*9

Page 29: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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/ / /

^ $<27 @

$<27 @

* 7 5

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*

ξ

ξ

∈ = = =

∈ =

= −

= −

7,IE@

ξ #+*2<*#***#(#)**2*1+*:)$2#/Ω ,

+))*7,IE@/2

^ $<2 7 @ 7 @

$<2 7 @

$<2 7 @

*9

*9 9 9 9 9

*9 9 9 9 9

ξ

ξ

ξ

∈ =

∈ =

∈ =

= − −

=

= −

7,I@

$(4$7, @/#+#29

^ $<2 7 @*

9 9 9 9

ξ

ρ∈ =

= − − +

7,I"@

W

/

B

B

!ρ=

= 7,IF@

**

7 @*

9 9 9

*9

ρ

=

=

Φ = +

Φ =

7,IG@

1 2Φ = −Φ + Φ 7,E!@

Page 30: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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Φ **($$292#+)## /))$29**$1*2$

Z Z

7 @/

B B B B

B

% ! % !=

Φ = + 7,E@

W%B#+*2<()',

Φ )$**2P2***$1

7 @

Y7 @

*9

/

B

B

! 9

ρ=

=

Φ =

7,E @

7,E@7,E @/)++(27,E!@**$1

/

B

B =

Φ = Φ 7,EH@

$(

Z Z7 7 @@B B B B B B! 9 % ! % !Φ = − + 7,EI@

#+)#$9#!B,

$#*+29*2#+)#$*)$**($(*+)$+

^ $<27 @B

B B!

!∈Ω

= Φ

7,EE@

*)**2#)#7,EI@7,EE@**$1

Z Z

$<27 @ $<27 7 7 @ @ @

B B

B BB BB B B B

! !

% %% %9 ! ! !

9 9 9 9∈Ω ∈ΩΦ = − + + −

7,E@

*2

$<27 @ $<27 @B B

BBB B

! !

%%9 !

9 9∈Ω ∈Ω

Φ = − −

7,E"@

#W

^ $<27 ] @

B

B B B!

! ! %∈Ω

= −

7,EF@

$(

Page 31: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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] BB

%%

9= 7,EG@

$ $*#* $* # ]B% 92 )P ($(+* )$ #+(#/ 2 #2

$*1$(2#*2**&*+2*,

*++#!!'

$* $)(+###+(2#**&*+2*: $ +()2/*2 ($$ *9

(2(2*)$*()$+(),'+4#**$*<++$22*+*,$

)28/$+4##2(4+/$)**2)$)*+)$#/*(9222**

)$$8*#($$#+2+)$*+9(#$L#**&*)2*,(2

)+*2(+2##22#+2211:22*$,

$#+9#$***($*(2+*)+(+#/*2$2#($$*)$*%*

)+(2*#$*$+$2+/$#'28+4#)+*$)**222+##+(2#2

(4+#*&*$**2$2#($$$++ 2#2#$*NIO3NEO,*$*+

*$#$2#211+2,

&$ 1$2 ** )* #$* ($* #* *&*8* 72< ) 2< )@/ $

#$# ++ $#$)+ $ ($* # *&*8 #$2 NEO3NO )2*<++$2*+ : * * ($*

N"O3NGO,$*)2)*/*#*$)Q#$#+(2$*+*$

#$2#211+2#$**22'*+(21*1+9(/9*$*+#

*2$'($*#*22'*+(21*1+9(,

=2<,E&)29#2$2*3$*

Page 32: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

6.CDD

'"#(

I

!!" #$ %&

(*2#8*&*8#&))2:)2712<,E@W*++*2$2 H/ / /,,, :

$ *2 # $ *( * #+* *&*30 H/ / /,,,! ! ! )$ <) # 2*

*((**21*,

$ #$2 #211+230 (*2* : 1$2 (*)# : $ *2 #* *&*

#+*30/#**&* H/ / /,,, /#$28:(9*& #+

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#*&3092*:+#((##$2#211+2,2

Z' −= 7,!@

)2*&*!**))*+(#$$()#+(#$<,

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- = + 7,@

W - *(112(2#($$*))*+(*$*##$)+2##*&/

* *& +2* : 2*$ / ($$(+2* 2 $( # & #

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$+()2/*2+<2<2(*3:3#2*2

- = 7, @

#+(#$<)$**1$2*$$*##'*&*(*+(21*/$

Z Z

Z

7 @ 7 @

'

- -

-

-

− −

=

=

=

7,H@

2) ' /*2 Z$<7' @ $<7 @ θ −= = $* ' $

θ= ,

2*2)#+(*&&+/$)$**2#*2($$*2*))*92

*(*$*$2*#'*&*(*+(21*,

Page 33: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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(#$<#211+2*)$23)$++2#2)$5,$J4$NIO3NEO,'2*(

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# *& )2* 2 $ ($2**$( # ($$ $ 2+ '*2 # ( +4# #

#+(2$'($*#$*2)*,

$* ($* # *&*8 ($**29 #$2/ * (112(2* # ($$ +$ (*/

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$2,92*$())**2)92(*2#+#(2)*#2(

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=2<,#211+2

() #+ # *&* 7 / @ − # $ (*$2 0 )$ ')/ *

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*)#( *2#$*) )+*#$2829(#+ χ #

Page 34: Université de Limogesaurore.unilim.fr/theses/nxfile/default/241afd90-c... · ˇ ˙’)’˚ * ˇ+’,’˚- ). /0, 1 2334 222 ˆ,˙ +* ˇ $ *# **2˛ ˇ$ 2 ˘* ddddddddddddddddddddddddddddddddddddddddddd

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(#+* 7 / @ + + #$* $ $* 4+ ( ) ( ) ! / ! 2 1$2*$

(*)#**(#+**2$*

Z Z

,

,

+ − +

+ + −

= + = − +

7,I@

2 7 / @, , *(*/)#+2#$2829 7 / @ + + )$$$2

Z Z 7 / @ 7 / @ 7 / @ , , + + − −= + − 7,E@

() 7 / @, , #+)# #<) # 2* $ # () 7 / @ − , ( 11 $

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)2**$(#*2<$Q:$*))$<$2#$**)$(2##2*$(*

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!! !7 @ H /I !< 7 @ !< 7 @ D = + + 7H, @

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#*2$)2**$(Q)$(9(9#$>((+,

1 )%

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9 *2<$+2*: 2*$#+)$)*2*(42*)**2*$2:#211+*

2*$*,4$9$%$$)2#/)4$*$#,($$(+2*($$/

2)*2*+2***2<$Q$))++)*2)*2#($$,

=2<H,#+2*$2#($$

$#+ ($$(8 $+$2# (* *2<$'/ $)2# $)4$*# *2<$ +*$

$2#$*)*#$**)$(1(2#$+)*2)*2#($$#$

)+2##+2**2#**2<$'(#+2#$*2**2,

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(*$/$+)*2)*2#($$*')2+)$

7 / @ 7 @ 7 @- τ α δ= 7H,I@

WR*$1(2#2$(S$2$()',

=2<H,H$)$##(4+(#($$

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*#+)$

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ττ =

=

=

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+$)#$+)*2)*2#($$$)+($&)

τσ τ τ= − 7H,@

$(

"

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ττ =

=

=

7H,"@

$$<#$##($$*#+122)$$$##(4+(9

E

σ

= 7H,F@

*2<$*+2*$2#21$2*(*2+#(*92)P*#+122*)$

#+ $<#$#,+$ ) $#$'2$h # $

+)*2)*2#($$)#(*2#+#'($*)**2*#2$(2##

$(2

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+$ ) # ($$ * *$* (*+9( * *&*8, $* #$2

1+92i($$*#2*+(211+9(1$1$#2<,

=2<H,I')#*2<$')$2*))*+*

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7 / @ 7 @ 7 @

$ $

$

- τ α δ τ=

= − 7H,G@

Wα$7@T$#+*2<$)2#()'$##$#$%,*(112(2*α$7@

* )$* 2+* 7H, G@ 9 * #211+* ()*$* # -7 τ@ *+$2** #

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=2<H,')#+)*2)*2)($$*+(211+9(

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*2$$<θ$#2(2#$2**(##$2$#+(),

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(*

D θ

λ= 7H,!@

$<θ*$+$2:($*#($$(8 2)+2*2#*$<*#*#211+* $%*92

)(4$<#$*)*()#*#211+*%*2$*,

$$$'2$#D+

$'

D

λ= 7H,@

)##+122$$##1+9(+D#$)*#*#*Q*

$' $'N OD " " + D D D D= − + 7H, @

$2$2 # $ 1+9( # $ )* ) P $**22+ : #$2 #

1+9(92$<2**2<$*2)$(#*+($*(*$+*,$()$$2*#$

1+9( )* D" # #+($$< D ) #2' $))+(2 2(2#( # 11

)),

2 D * +<2<$ #$ D" 7D ii D"@ $* 11 )) * )$* )Q 1

+$2***#2K1$#2<,

2 D * )$* +<2<$ #$ D"/ $ +)* 2)*2 (4$<$2 $() )*

$)2# * #+ )(4 # ( # #' *&* +$2** * #2

$)2#1$*1$#2<,#+122$$)2#2+#+$2**/#+122$#+$$

(4$<#($$$))'2$2)$)*#(4+(7H,H@92(*)#

:$#+)#$$9*)$$8*#($$*)$292$2$*,

(+$2###!,E/*#+)$

$'

G

= 7H,H@

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*2<$,

#@ $$ *+(21 1+9( : +$2** $)2# # 2<2 $<$2*

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$<#$##*2<$)*#(4+(*21+2:$#+#*2<$,

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=2<H,"+($)2$21*#*&)*#($$':+$2**

" &6 2-

*2*1(2*)P 22*+* ) # #* $))(4*##8* *$2*29*

#($$,)4+892*2+**)*2(2*(2#*+$2***:)2

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7 @ α η= + 7H,I@

WE*2<$**2*2<$$*2*,

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7 @ ')7 @

,

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σ σ−= 7H,E@

W*)*221U+($&)#$)$2+#$)$22$<2$2#S.

• *92&$ 2<##2( + +()/ $&# $

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$$#2*22#2(##*2+#)$22+

!

7 @7 @ ')7 @ 7 @

,

) )D +

σ σ σ− += 7H,@

$())*221**,

))+*$)2#$'2$#*2<$#2$+3*$1(2#212+#**

#)28*)8(##>+,)$9$2*+97H,E@*2)Y!

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++(),

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#*$2*29#($$*+(211+9(*+$+:)$2#(2#($$

*+(21 1+9(, 11 #8 2+$2 # ($$ *+(21 1+9( *

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# $,$* ($*#*&*8$ 2 *)+*) $%* ** $

1

!

7 / @ 7 @ 7 @

$ $

$

- τ α δ τ−

=

= − 7H,"@

* #211+* $%* +$ 2#+)#$*/ 2 * #P # $ #2*22 #* $2$*

$+$2*S$,$*(#2<##2(/*(*(112(2*$#2*22

$+$2<$**2#&,

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)+*( # 2< # #2( 7 2313*2<4@/ ')**2 7H, G@ * )+*

(*2

7 / @ 7 @ 7 @ 7 @

$ $

$

- τ αδ τ α δ τ−

=

= + − 7H,F@

WS#+*2<1$(#$+$2#$2<##2(S$$()*$#+)#$

#)*#)4+8#$%2)*($$(+2*$+$2**:)2+(4,

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=2<H,F+)*2)*2#($$:+$2***()*+#2*$%*

%%!3$!4! "!""''"

1"!! 1'!&'!

$*2**2 * $11(+ #$28 # $ )$ ($$ # $*2**2,

*2$2#($$*;(42($#$*)(***##+(2(4+:

$+()2$$$*2**2#21$2,$*+(**$2#$$)*9*

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$* )+(+# 9 () # ($$ *1(2 # )*,

#*2$2#($$$2**)+*$<$'#)*++##+(2,2$$$

#($$#*&*8+4#$#+9$*2)*))*<$#)+(2*2#$*

*2$2#*)$$8*#(#2,*2$2)P1$2#$28$<*

$ $* # ))2++* *$2*29* #* #+* $*2** : $2# # *+9(a)2*

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#($$*)(2,

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)(*** # #+(2 : $ +()2 * +*+ )$ $ 12< H, G, ' (* *

)+*+*, ( # #+(2 # #+(#$< ')2 * (112(2* *2+* )$ (

#*2$2#($$)*2*2$2#*#+*+2**,*2*($*#12<*

)*)+**&)#($$,

=2<H,G(4+$#*2$2#($$##+(#$<:$+()2

!!6

')**2 # *2<$ Q * ( # 7H, I@, *2$2 # ($$ * $*+ * $

($2**$(#*+9(#)2*29)+&+$(($2

)+2#2(2+*2$$$#+$2**,

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=2<H,!')#*+9(#$L#$*$2#21$2

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(*$*($2#(*/#'$))(4**<++$22*+*2*$<2

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Z

Z

^ 7 @

5

5

α=

= 7H, !@

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Z

Z

^ 7 @

7 @

5

**'

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ασ=

=+ 7H, @

*#211+*+4#*2#2*#*2$29

*#211+*+4#*2#2*#*2$29

α α δα= + 7H, @

9$#$29#*2$2#($$*#+)$

Z^ ^ ^7 @7 @ασ α α α α= − − 7H, H@

W7,@Z#+*2<')**2(%<+#7,@,

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Z

^ ^7 @7 @

5

5

σ α α=

= − − 7H, I@

• -2(3"$!)'*"$)5#

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(429*#*2$2#($$$**#a,*2$*)$

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Z^ ^N O ' 7H,EF@

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Z^N O' 7H,EG@

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