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7.2 $u_{-}<u_{+}$ $B$N$H$-(B

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$B?^(B 22: $BKDD%GH2r$HFC@-6J@~(B

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$B:#!"@5$NDj?t(B $\lambda$ $B$KBP$7$F(B

$$w(t,x)=u\left(\frac{t}{\lambda},\frac{x}{\lambda}\right)$$

$B$H$*$/$H!"(B$w$ $B$b17) $B$rK~$?$7!"(B $B=i4|CM$O(B $w(0,x)=f(x)$ $B$H$J$k!#$=$l$O(B

$$\begin{eqnarray*} w_t+ww_x & = & \frac{\partial }{\partial t}u\left(\frac{t}{... ...c{x}{\lambda}\right) = f\left(\frac{x}{\lambda}\right) = f(x) \end{eqnarray*}$$

$B$H$J$k$+$i$G$"$k!#$h$C$F!"0l$D$N=i4|CM$KBP$7!"2r$,0l$D$K7h$^$k$Y$-$@(B $B$H$9$l$P(B $w=u$ $B$G$"$k$3$H$K$J$j!"$D$^$j$9$Y$F$N@5$N, $t$ $B$H$9$Y$F$N $B$KBP$7(B

$$u(t,x)=u\left(\frac{t}{\lambda},\frac{x}{\lambda}\right)$$ (27)

$B$,@.$jN)$D$3$H$K$J$k!#:#!"$3$N<0$K$*$$$F(B $\lambda=t$ $B$H$9$l$P(B

$$u(t,x)=u\left(1,\frac{x}{t}\right)$$ (28)

$B$H$J$k$N$G!"(B$u$ $B$N(B $t=1$ $B$N$H$-$NCM$r(B $v(x)$$B!"$9$J$o$A(B $v(x)=u(1,x)$ $B$H$9$k$H(B (28) $B$K$h$j(B

$$u(t,x)=v\left(\frac{x}{t}\right)$$ (29)

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$$\begin{eqnarray*} 0& = & u_t+uu_x\\ & = & \frac{\partial }{\partial t}v\left(... ...ght) \left\{-\frac{x}{t}+v\left(\frac{x}{t}\right) \right\} \\ \end{eqnarray*}$$

$B$@$+$i!"(B$y=x/t$ $B$H$*$/$H(B

$$v'(y)\{v(y)-y\}=0$$

$B$H$J$j!"(B$v'(y)=0$ $B$H$9$k$H(B $v$ $B$,Dj?t$K$J$j!"$h$C$F(B $u$ $B$,Dj?t$K(B $B$J$C$F$7$^$C$F5a$a$k$b$N$K$J$i$J$$$N$G!"7k6I(B

$$v(y)=y$$

$B$3$H$,$o$+$k!#$h$C$F(B (29) $B$K$h$j(B

$$u(t,x)=\frac{x}{t}$$

$B$,F@$i$l$k!#$3$N2r$rFC@-6J@~$N6uGr0h$KKd$a$F(B

$$u(t,x)=\left\{\begin{array}{ll} u_{-} & (x<u_{-}t), \\ \... ...eq x < u_{+}t), \\ u_{+} & (x\geq u_{+}t) \end{array}\right.$$ (30)

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