(PDF ¥Õ¥¡¥¤¥ë: bib.pdf)

1.4 lecture note

$B9V5AO?$N$h$&$J$b$N(B:

G.-Q.Chen [2],
B.Dacorogna [10],
L.C.Evans [16],
J.Smoller [32],
L.Tartar [37],
J.Mlek, J.Neas, M.Rokyta and M.Rika [24],
D.Serre [30]

[2] (G.-Q.Chen) $B$O(B [11],[12],[1] $B$N(B $B7k2L$r$[$\$^$H$a$?$b$N$G!"(Bisentropic gas $B$K$D$$$F$NJ}K!$rCN$k$J$i$3(B $B$l$rFI$`$N$,0lHV$N6aF;$G$O$J$$$+$H;W$o$l$k!#$^$?!"(Bscalar $B$N(B Tartar's functional equation $B$N(B Tartar $B$N2rK!$r>/$74JJX2=$7$?$b$N$b:\$;$F$$$k!#(B

[10] (B.Dacorogna) $B$O(B conservation law $B$X$N1~MQ$r0U<1$7(B $B$F$$$k$H$$$&$h$j(B weak continuity $B$rD4$Y$k$3$H$rL\I8$H$7$F$$$k$h$&(B $B$G$"$k!#$7$+$7(B

Chapter . Compensated compactness
Chapter . Applications
Nonlinear conservation laws

$B$N$h$&$K(B scalar conservation law $B$N$X$N1~MQ(B (Tartar $B$NJ}K!(B) $B$b!"(B Tartar's equation $B$N2rK!!"6a;w2r$NI>2A!">ZL@$NN.$l$J$I$b4^$a$F(B $Be$2$F$$$k!#(B

[16] (L.C.Evans) $B$K$O(B conservation law $B0J30$K$bBJ1_7?$NJ}(B $BDx<0$X$N1~MQ$J$I$b=q$+$l$F$$$k$h$&$G$"$k!#(B conservation law $B$K$D$$$F$O(B scalar $B$NJ}Dx<0$@$1$G$J$/(B [14] $B$K$D$$$F$b$*$*$^$+$K?($l$F$$$k!#$^$?!"(BYoung measure $B$NB8:_DjM}$N(B [36] $B$K$D$$$F$b(B $BCzG+$K=q$$$F$"$k!#(B

[32] $B$O(B 2nd edition $B$N?7HG$K$J$C$F(B

Chapter 25 Recent results
A compensated compactness

$B$re$2$F$$$k!#>ZL@$O$[$H$s$I=q$$$F$$$J$$$,!"(B[36], [14] $B$N4JC1$JN.$l$r:\$;$F$$$k!#(B

[37] $B$O(B Tartar $B$K$h$k(B [36] $B$H(B [14] $B$NItJ,E*$J>R2p$G$"$k!#(B

[24] $B$K$O!"(BYoung measure $B$r2r$H$9$k(B measure valued solution $B$NOC$,(B $B=q$+$l$F$$$k!#(B

$B$^$?!":G6a(B Serre $B$K$h$k(B [30] $B$,=PHG$5$l$?!#(B $B$N(B Chapitre 9 $B$G(B compensated compactness $B$,e$2$i$l$F$$$k!#(B