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Next: 1.2 $B:9J,K!J}Dx<0(B Up: 1. $B Previous: 1. $B

1.1 $BGHF0J}Dx<0(B -- $B4JC1$J@bL@(B

$ t$, $ x$ $B$H$$$&(B 2 $B$D$NFHN)JQ?t$K$D$$$F$N4X?t(B $ u=u(x,t)$ $B$K$D$$$F$NJ}(B $BDx<0(B

(1.1) $\displaystyle \frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2 u}{\partial x^2} \qquad\hbox{($x\in(a,b)$, $t>0$)}$

$B$O(B $ 1$ $B1.1($B$3$3$G(B $ c$ $B$OM?$($i$l$?@5$NDj?t$G$9(B)$B!#$=$l$O!"$3$NJ}Dx<0$,!$0lMM$J(B $B89$N?6F0$d!$:Y$$4I$NCf$N6u5$$N?6F0$J$I$N!"0l]$rI=(B $B$o$9$b$N$G$"$k$H2rl9g$O(B $ u(x,t)$ $B$O;~9o(B $ t$ $B$K$*$1$k!"89>e$NE@(B $ x$ $B$ND`$j9g$$$N0LCV$+$i$NJQ0L$rI=$o$9$b$N$H9M(B $B$($^$9!#(B

$B $B$OGH$NEAGE$NB.$5$K$J$j$^$9$,!"0J2<$G$O;~9o$NC10L$rE,Ev(B $B$K $B$r?7$?$K(B $ t$ $B$H$9$kJQ?tJQ49$r9T$&!K$3$H(B $B$K$h$C$F(B $ c=1$ $B$G$"$k$H$7$F07$$$^$9(B1.2$B!#F1;~$K(B $B6u4VJ}8~$K$D$$$F$bF1MM$NJQ?tJQ49$r;\$9$3$H$K$h$C$F(B $ a=0$, $ b=1$ $B$H2>Dj(B $B$9$k$3$H$b=PMh$^$9!#(B

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(1.2) $\displaystyle u(x,0)=f(x) \qquad \hbox{($0\le x\le 1$)}$

(1.3) $\displaystyle \frac{\partial u}{\partial t}(x,0)=g(x) \qquad \hbox{($0\le x\le 1$)}$

$B$H!"3F;~9o$G$N89$NN>C<$N>uBV$r;XDj$9$k6-3&>r7o$r2]$9$3$H$K$h$j!"2r(B $ u$ $B$,7hDj$5$l$kLdBj$H$J$j$^$9!#(B $B6-3&>r7o$H$7$F$O!"(B $BN>C<$,8GDj$5$l$F$$$F(B ($B4I$NCf$N6u5$$N?6F0$N>l9g$G$O!VC<$,JD$8$i$l$F$$$F!W(B) $BJQ0L$,>o$K(B 0 $B$G$"$k$H$$$&(B

(1.4) $\displaystyle u(0,t)=u(1,t)=0 \qquad \hbox{($t> 0$)},$

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(1.5) $\displaystyle \frac{\partial u}{\partial x}(0,t) =\frac{\partial u}{\partial x}(1,t)=0 \qquad \hbox{($t> 0$)}$

$B$r9M$($k$3$H$K$7$^$7$g$&!#(B $BG.EAF3J}Dx<0$N>l9g$HF1MM$K!"(B (2.3.1) $B$r(B Dirichlet $B6-3&>r7o!"(B (2.25) $B$r(B Neumann $B6-3&>r7o$H8F$S$^$9!#(B


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Next: 1.2 $B:9J,K!J}Dx<0(B Up: 1. $B Previous: 1. $B
Masashi Katsurada
$BJ?@.(B14$BG/(B11$B7n(B29$BF|(B