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5 $2T$-$B<~4|$r;}$D87L)2r(B

$B:G8e$K$R$H$D87L)2r$G$"$k(B $2T$-$B<~4|2r$r>R2p$9$k(B.

$u(t,x)$ $B$H$7$F?J9TGH7?$N4X?t(B

$$u(t,x) =\frac{1}{T} + a\cos\left(2\pi x - \frac{\pi}{T}t -\frac{\pi}{4}\right)$$ (9)

$B$r9M$($k$H(B

$$g(t,x) = u_t+\left(\frac{u^2}{2}\right)_x = u_t+uu_x = \pi a^2 cos\left(4\pi x -\frac{2\pi}{T}t\right)$$

$B$K$h$C$FDj$^$k(B $g(t,x)$ $B$b?J9TGH$G$"$j(B, $B$$$:$l$b0\F0B.EY$O(B $1/(2T)$ $B$G(B, $u$, $g$ $B$N(B $x$-$BJ}8~$N<~4|$O$=$l$>$l(B 1, $1/2$, $u$, $g$ $B$N(B $t$-$BJ}8~$N<~4|$O$=$l$>$l(B $2T$, $T$ $B$H$J$C$F$$$k(B. $B$D$^$j$3$N(B $g$ $B$KBP$7$F(B $u$ $B$O3N$+$K(B $2T$-$B<~4|2r$G$"$k(B.

$B$3$N(B $g(t,x)$ $B$KBP$7$FA0@a$^$G$NJ}K!$HF1MM$N?tCM7W;;$r$7$?$b$N$,(B Fig. 7,8 $B$G$"$k(B.

$B?^(B 7: $u(mT,x)$: $m$=0,1,...,30,
$L=1000$, $u(0,x)=1.0$
($T=0.5$, $\pi a^2=1.0$)

$B?^(B 8: $u(mT,x)$: $m$=100,101,...,130,
$L=1000$, $u(0,x)=1.0$
($T=0.5$, $\pi a^2=1.0$)

$B$3$3$K$OITO"B3@-$r;}$DJL$N?J9TGH7?$N(B $T$-$B<~4|2r(B

$$u(t,x)=\frac{1}{T}+\left\{\begin{array}{ll} \displaystyle ... ...T}t-\frac{\pi}{4}\right) & \mbox{$B$=$l0J30(B} \end{array}\right.$$ (10)

$B$,$"$i$o$l$F$$$k(B.

$B=i4|CM$r(B, $B:#$^$G$N$h$&$JDj?t$G$O$J$/(B, (9) $B$N(B $u(t,x)$ $B$K(B $t=0$ $B$H$7$?$b$N$rM?$($?>l9g$N(B, $u(mT,x)$$B$N%0%i%U$,(B Fig. 9,10 $B$G$"$k(B.

$B?^(B 9: $u(mT,x)$: $L=1000$,
$m$=500,501,...,530, and
$m$=2000,2001,...,2030,
u(0,x) is given by (9)

$B?^(B 10: $u(mT,x)$:
$m$=2000,2001,...,2030,
$L=1000$, and $L=3000$,
u(0,x) is given by (9)

Fig. 9 $B$O(B $L=200$ $B$H$7(B, $m=500$ $B$+$i(B $m=530$ $B$^$G$N(B $B%0%i%U$H(B $m=2000$ $B$+$i(B $m=2030$ $B$^$G$N%0%i%U$G(B, Fig. 10 $B$O(B $L=1000$ $B$H(B $L=3000$ $B$N>l9g$N(B $m=2000$ $B$+$i(B $m=2030$ $B$^$G$N%0%i%U$G$"$k(B.

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