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p SAC - creden - Université Montpellier I

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I5!>)$*,-)$!)3?%*,->!Xd5Y!%.,!-18%.! +1-2)$*,-)$!)3?%*,->!1%.,%!<br />

254534%@! ^%! 45! 8j8%! >5Z)$C! 45! >)18045,-)$! /0! +1)34H8%! >5-,! 49]K+),]H.%! F0%!<br />

,)0.!4%.!*)$.)885,%01.!/%!,K+%! r !.%!>)01$-..%$,!50+1H.!/0!MDL@!L-!)$!5!<br />

p = c + k = p C!*%1,5-$.!*)$.)885,%01.!2)$,!*])-.-1!4%.!>-18%.!+1-2)18045,-)$!/%!45!>)$*,-)$!)3?%*,->!1%.,%!254534%@!(1%8%1!(1)4+7!PQRRdT!<br />

+).%$,!F0%!Xd*Y!$9%.,!+5.!.,1-*,%!/5$.!45!.)40,-)$!)+,-854%@!!<br />

!<br />

L)-,! λ<br />

1!4%!I5B15$B-%$!/0!+1)B1588%!QC!52%*! λ !4%!804,-+4-*5,%01!5..)*->)$*,-)$!/%.!251-534%.!/%!<br />

/-%1C!)$!)3,-%$,!4%.!*)$/-,-)$.!/%!+1%8-%1!<br />

)1/1%!.0-25$,%.!'!<br />

!<br />

∂ λ1 q1<br />

r m<br />

q1<br />

u m<br />

= α( −q1r) − q1 u<br />

+ λ ⎡ ( p1 c1 r<br />

k) ( p1 c1 u<br />

k)<br />

q1<br />

r<br />

qju<br />

0<br />

m ⎢<br />

∂ − − + ∂ − − + + ⎤<br />

m m<br />

⎥ = ! Xb5Y!<br />

∂p1 ⎣∂q1 p1<br />

⎦<br />

∂ λ<br />

∂p<br />

= α( − q<br />

q<br />

r m<br />

) + λ ⎡∂<br />

( p −c − k)<br />

+ q<br />

⎥ = 0! !<br />

⎣<br />

⎦<br />

! ! ! Xb3Y!<br />

!<br />

1 2<br />

m<br />

2r ⎢ m 2 2r 2r<br />

2<br />

∂p2<br />

(1%8%1! (1) 4+7! PQRRdT! $),%$,! F0%! 49-$,%1+15-,!/0!$)831%!/%!+)..-3-4-,H1%$,!F0%!+51!4%01!4)*54-.5,-)$@!!<br />

!<br />

(%,,%!.-8+4->-*5,-)$!.9%&+1-8%!/%!45!>5Z)$!.0-25$,%!'!<br />

S ( q , q ) = S ( q , q )!+)01!,)0.!( q , q )@!<br />

r<br />

1 2 u 1 2<br />

1 2<br />

! kkkg!

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