On Uniqueness and stability for systems of conservation laws
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(219) 1 I CH 8 # @ TQUZ \ Lc.LNVH[ZTQS`V_LNV #SHeJTQc VHM \dc.SHe#\mOi\dgghL X PS$ 0 021' G 2Q( / H I 2 452 + J 0)$+B( )I:A, (B+-,@:A@ 0QL( > 6D+ 82,?J#:A+-, ( TCO2Q( (*)32 5:A, GA+B(B+B:8,#0 DL DL
(220) ) :ACNG <Q:AE0: /2 : + ;: L )32, <Q:AE 2> ) ; : :A,2)3>H0 OQ TQg cH f
(221) , (
(222) 2 # NXIH 69cHcHfJg\ >MPU SHe#\( MPU S`V_LNV CSHeJLNSbSHe#\^VH\k\ #TQc`SHc : LUJj c`\ f#\dUJ \dc 2 2 2 > Zc_fJ _eSHeZLNS
(223) (
(224) 2 : NXIHH WrMV\ \^V ! NXE= M
(225) SHe#\ TQj#\dLc Lc_cHfJgp\ ! bWrMVLOQO SHe#\ MSHe#\^V ^LcH\dc[ \dTQU#n3\dU SHTiV_\dNO cHTQghTQOQLNVdX 'a (SHeJ%\ ! T c_ _eJTiS MPU SHTQU fJTiS V_M \dj TQU NX \meJL \ ' () ( () ( ) ( ) / " 2 ( 2 NXIH WrMV/c`MPgp\3 MPUJc`SHLU S " JWlMV/\ \^V <() !hLUJj \ \^V TQU S`\^V LO H I X7;YS.TQc.UJMSVH\dc`S`V_T SHT \tS`M LcHcHfZgp\ " : XC=.e#\tLcHcHfJg SHTiMPU NXQ^ T g OQTi\dc OQ TQg ' () ( () # NXI8H S /. . . . . . 3.
(226). . . !. . . . . . . . ! . . . . . . . . #. . . . . . . . . 3. . . . . . . (. (. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (. . . . . (. . . . .
(227) . . . . . . . . . . .
(228) H. /z . . M \ \^V TiW NXIHH e#MPOQjJc [ NXIH TiSWrMPOQOiM c. $. . . . . &. . . . . . . . ) (. . ) . ! . . '
(229) (
(230) ( " ( 2
(231) ( ,2 ! ( " (
(232) ( ( " JTQU MPU S`VLjJTQ SHTiMPU TiSHe NXIH8S X7=eJTQc VHM \dcSHe#\Oi\dggL X . . . . . NXIH[ . . . WrMV.LOQO D"%"N16( cG W , G$2QE (*)32 0> /2 >H0505@3 J(B+ :A,#0 :=< 2
(233) > DL L (*)32 0F(7>D( 2F0 . . DL DL 0>8(B+-0-< . . .
(234). . .
(235) . +-, NXIH . '
(236) (
(237)
(238) # ;<UJj#\^\dj#SHLA TQU#n LUZj Oi\^S`SHTQU#n 2
(239) TQU NXIH MPU#\tM[ZSHLTQUJc
(240)
(241) D (% / OQT g cHf '
(242)
(243) D (% )
(244) ' ) (% #. .= e#\ MSHe#\^V.TQjJ\dU SHTiSR(T c VHM \dj%cHTQgT OQLNV_ONX PS$ 0 0`1 cG cX 2Q( 452> 2>H.%0Q:AC @3(B+ :A, : < DL 8L 2Q( (*)32 5:A, GA+B(B+ :A,#0 DL DL
(245) ) :ACNG >8( 3. 0Q: /2 J3:A+*, ( 2 @>8(B+ :A,#0. .
(246) L. . )32, (*)320F(7>D( 2F0. . . . >A, G (*)320 J#2I2IG; 0>8(B+-0-< (*)#2 A> ,#.H+-,2 @D6$:A, +B:8(. . NXIH . ; (% 5 (* #. . = Mn\^SHeJ\^V TiSHe SHe#\\dU S`V_M MPUZjJTiSHTiMPU T U G !G\dghgLNX XKS(cHe#M c/SHeJLNS.SHe#\3c`SHLNS`\dc LNVH\t MPUJU#\d S`\dj\dTQSHe#\^V[9(LULjJgTQc_cHTi[ZOi\/cHe#M (MV[9(Lp MPU SHL S9jJTQcH MPU SHTQU fJTiS VHM LNnPLNSHTQUJn TiSHec \^\dj:;GX = M VHM \tSHeJ\mOi\dggL JjJ\ ZU#\KSHe#\tW fJUJ SHTiMPU TiW > ;.M 7 # TiW 6:L;.M#. . . . . . . . . !
(247) !. 3. . . . .
(248) z a' NXQ^ TiSWrMPOQOiM c 2 2. &. . ,. . &. O TQg WrMV\ \^Vk[ MPfJUJj#\djkc`\^S . . WrMV.LOQO . &. HH. . .
(249) 7
(250) ( 7 4 X MV_\^M3\^V NX TQg OQTi\dc. .
(251) M
(252) 7
(253) 1
(254) 7
(255) 8 7 \ LUJjLOQO : XE=eJ\ S MhLN[ M3\mV_\dOQLNSHTiMPUJcTQg ON
(256) TiSHc`\dOiWZT c LKc`MPO f#SHTiMPU3MW NXQ XE=.e#\^VH\^WrMVH\CSHeJ\D.LU#. cHe#M QT U#n9SHeJLNS>SHe#\7W fJUJ SHTiMPU TQU#\ $ f#nMPUJTiMS \ fJLNSHTiMPUJc NXIH g3fJc`Se#MPOQjGX 6 \ MPUJ ^O fJj#\SHeJT cCc`\d SHTQMPUh[ pVH\d ^LOQOQT U#ntS MbOiM ^LO]TQU S`\^nV_LO \dc`SHTQgLNS`\dc&SHeJLNS& _eJLNV_L S`\^VT ^\ SHe#\ S`V_>L <`\d S`MV_Ti\dc/MW L
(257) @ SHLUJjJLNVjD.Ti\dgLUZU@ \dgTinVHMPf X = MRS \dc MW OQM ^LOPL VHM #TQgLNS`\Cc`MPOQf#SHTiMPUZc WlMV NXQ TQO Oy[ \E MPUZcHTQj#\^VH\djGX IKU#\TQc j#\^V_T \dj WrVHMPg SHeJ\/c`\dOiW wcHTQghTQOQLNVEc`MPO f#SHTiMPUMWGL3D.TQ\dgLUJU VHM[ZOi\dg SHe#\.MSHeJ\^V7T cM[JSHLTQUJ\djh[ <WlV_\^\ dTQU#n SHe#\K M A\ B
(258) ^Ti\dU SHc&MWGSHeJ\9 MVHV_\dc MPUJjJTQU#n fJLcHT OQTQU#\dLNV&$e \^VH[ MPOQTQ c c`S`\dg TQU
(259) L3U#\dTinPe [ MV_e#M M jMW LpnPT \dU MPT U S^X ! \^S / ;2 + []\(L$U WrfJUZ SHTiMPU LUJj # L9U MPT U S L e#\^VH\ eZLcL <HfJg X57LOQO () SHe#\ fJUJT f#\.cH\dOiW wc_TQgTQOQLNVE\dU S`VHM
(260) cHMPOQf#SHTiMPU
(261) MWGSHe#\ D.TQ\dgLUJU VHM[ZOi\dg ( TiW > G
(262) ) NXIH TiW : G#
(263) D !G\^ S ; [ \tLU f \^V7[ MPfJUJjkWrMVSHe#\LN[Zc`MPOQf#S`\ NLOQf#\dc7MW>LOQO L \3c \^\djJc^X #MV ! Zj#\ ZU#\ Ti0W 2 ( 2 / ;G # (
(264) () NX P TiW02 ( 2 : ;G X I9[ZcH\^V \
(265) SHeZLNSSHe#\kW fJUJ SHTiMP*U 2 ? TQc ! T cH _eJTQS
(266) MPU SHTQU fJMPfJc X VdX S^X SHe#\ P]\ jZTQc`SHLUJ \ LUJj L VHMPL _eJ\dc 1L# c 2
(267) X 8/\ S ^LOQO 9 1 8 SHe#\ 8PL M[ TQLU gLNS`V_T )MW MPg f#S`\djLNStSHe#\ MPTQU S X #M,V ! j#\ U#\ ) Lc/SHe#\3c`MPOQf#SHTiMPU MW>SHe#\OQT U#\dLNV/9e \^VH[ MPOQT 5LfJ _9e VHM[ZOQ\dg TiSHe MPUJc`SHLU S/ M A\ Bh ^Ti\dU SHc # NX J .
(268) !. . #.
(269). . . . . . !. . . +!. . . . . . . . . . . . . . . . . . .
(270). . . . . . . . . .
(271) . . .
(272) H /z SP $ 0 0`1 cG 2Q( 4I2> 7( >A,GD>AE G +72
(273) >A, , 2 +N68E :A@ J 692,M2E >8( 2G;4(*)32"0 H0F( 2 $L +B(*) GD:>8+-, >H0;+*, DL AL )32Q, (*)32E2 2 8+-0F(*0?>?I:8,#0F(7>A, ( \ 05@ ) (*) >8(%(*)32%<Q:AC-CN: +*,96 ) :8C GH0QL :AE 2 A2QE <F@3,. (B+ :A, 2 A2E >A,G : +B(*) (*)32/>$4: 82 G$2 ,+B(B+B:8,#0 :A,M2) >H0 1 8 ( ) NX / \ ? :D(7L >8EL 1 I ( GH I
(274) H 8 1 8 ( ) NX FH / \ ? :8(7L >AEQL 1 = I (
(275) H 8 # #MVKL VHM MW Jc`\^\ H XE I X . &.
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