1、a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a20a21 6a22a24a23a24a25a24a26a24a27a24a28a24a29a24a30a24a31a24a32a34a33a35a24a36 f(t;x)a37 (t;x) a38a40a39a42a41a24a43 G a44a42a45a24a46a24a47a49a48a24a50a24a51a24a52a24a53a24a54a24a55a40a56a58a57a24a59a34a60a49a61a34a6
2、2 x2a63a24a64 2.1a65 x5 a66a24a67 5.1, a68a24a69a24a70 ( ; ) 2 G, a71a24a72a24a73 (E) a53a24a54a24a74a24a75a24a57a34a59 x( ) = a41a24a76a24a65a24a77a24a78a24a37a24a47a80a79a24a48a24a81a34a82a24a70a34a41a24a60a84a83a34a85a34a86a24a87a34a88a34a89a24a90x = (t; ; ):a36a88a24a41a24a78a24a37a40a91a24a39a4
3、2a90 (a( ; );b( ; ). a92a24a93a24a88a24a94a24a81S : t2 (a( ; );b( ; ); ( ; ) 2G (6.1)a95a41 n+ 2 a96a40a97a42a98a24a99a24a100a24a60a80a101a24a102a24a103 xa81a24a104a24a98a24a105a24a47a80a74a24a75a40a106a42a107x0 = x; x( ) = a41a24a77x = et a94a24a81 t; ; a108a24a109a24a110a24a111a24a98a24a41a24a99a2
4、4a100a24a60a112a24a113 6.1a114 f(t;x) a115 (t;x) a116a118a117a118a119a49a120 G a121a49a122a118a123a118a47a125a124a24a126a24a127a34a128a24a129a24a130a34a131a40a132a24a133a58a134a24a60a135 x = (t)a136 (E) a119a58a137a34a138a34a139a34a47a80a140 t a136a34a141a34a142a34a143a145a144a34a117a34a119a58a146a3
5、4a137a34a147a34a148a150a149a80a151a145a144a117a42a47a153a152a42a142a24a143 0, a154a24a155a40a156; j ( )j a157a47 (E) a119a49a158a118a137a118a139 x = (t; ; ) a159a161a160a49a143 t a162a118a147a118a163a118a164a118a47a80a165a42a124a24a166 (t; ; ) a136a149a42a120V : t ; ; j ( )j a162a40a119a42a122a24a12
6、3a24a167a24a168a24a60a108a118a110a118a66a118a67a118a169a64a37a24a67a64 a95a65a24a170a24a171a95a34a172a24a173a24a174a24a175a34a176a24a177a60a125a83a24a85a24a178a24a179a34a47a180a37a24a170a34a171a95a47a125a181a24a182a71a118a72a118a183a118a184a118a185a118a186a118a187a24a67a24a188a34a72a24a60a189a87a24a
7、70a24a110a24a187a24a67a40a106a42a107a24a190a34a191a24a181a24a182a24a71a24a72a24a41a24a74a24a75a40a106a42a107a24a105a34a47a189a74a24a75a24a57a24a59a81a118a192a118a188a118a193a118a98a118a194a118a66a24a41a24a47a189a79a34a193a24a98a24a195a24a196a24a197a24a198a24a199a24a200a24a68a34a201a24a194a24a60a35a1
8、02a24a74a24a75a24a41a24a181a24a202a24a203a34a204a24a205a24a206a24a207a24a208a68a118a170a118a41a118a77a118a209a118a210a118a41a24a111a24a211a34a47a189a92a24a93a24a212a24a213a24a214a24a41a24a74a24a75a40a106a58a107a24a41a24a77a24a215a24a171a24a216a24a75a24a217a24a218a24a209a24a202a34a60a173a24a219a24a95
9、a24a220a41a24a66a24a67a24a47a80a108a24a186a24a221a24a222a24a217a24a195a34a218a24a223a34a224a219a60a66a24a67 6.1 a41a24a199a40a225 a182a24a109a24a226a24a227a24a228a24a2291. a230a24a231a24a232a40a233a42a229a80a103 1 0 a234a24a182a24a202a24a105a24a47a153a235a42a43U : t ; jx (t)j 1a236a24a237 Ga44a42a47
10、a80a48 f(t;x) a237 U a95 a53a24a54a24a55a40a56a42a57a24a59a24a601a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a20a238a215a95a47a240a239a237a24a241a182a40a242a42a243a24a244 (t; (t), t2 ; a81 G a44a49a70a173a118a245a235a49a246a24a47a189a88a24a247 Ga41a248a24a245a41a
11、24a249a24a250a24a81a24a70a34a110a34a251a34a100a34a47a253a252a80a254a34a255a175a1a0 1 0 a54a3a2a24a202a24a47a80a217a24a196a3a4 U G, a48a40a239a237 Ua81 G a5a42a41a173a24a245a235a42a43a24a47a80a61a24a62a173a1a6a3a7a1a8a66a34a67a34a217a24a178a34a47 f(t;x) a237 U a95 a53a24a54a24a55a40a56a42a57a24a59a24
12、a602. a90a219a199a40a225a42a66a24a67 6.1, a83a24a85a24a171a3a9a24a226a3a10a3a11a1a12a34a60a84a83a34a85a1a13a1a14a34a196a34a199a145a225a58a229a84a103 0 a15a24a103a202a24a105a24a47 x = (t; ; ) a81a40a235a42a43 V a95 a185a24a70a17a16a42a45a24a46a24a99a24a100a24a41a24a70a1a18a1a19a6a60a84a199a145a225a42
13、a41a1a20a1a21a34a72a3a22a247 x2 a70a3a23a24a47a80a212a24a195a17a24a42a41a24a255a24a81a3a25a1a26a3a11a1a27a34a41a3a28a0a60a84a108a1a29a0a25a1a26a3a11a1a27a34a900(t; ; ) = ( ) + (t):a206a3a30a3a31a3a26a40a239k(t; ; ) = +Z tf(s;k 1(s; ; )ds; k = 1;2; (6.2)a194a24a66 k a26a3a11a3a27 k(t; ; ). a0 0, a4a2
14、4a2140, a4a24a214 x = (t; ; )a237a235a42a43V : t ; ; j ( ; 0; 0)j a95a45 a46 a47a92a91a94a93 a217a24a37 (t0; 0; 0)a95 a45 a46 a60 a239 a254a96a24a49a105a44a97a24a86a44a98a161a233a49a47 (t0; 0; 0)a81 Sa41 a44a99a88 a47a45 (t0; 0; 0) a41 a234 a182 a202a94a100a118a43a161a44a42a69a44a101a3a88 (t0; 0; )
15、a172 a37 S a5 a60 a108 a81 a252a49a90a118a103 (t0; 0; ) a234a182a44a102a44a11 (t0; 0; 0) a105a118a47a189a83a118a85a173 0 (a38a176 0 2 ( ; ), j ( 0; 0; 0)j ,a103 (t; 0; ) a104a1a105a34a37 t a95a34a173a66a177a47a39a45 ; (a( 0; );b( 0; ). a106a34a79t0 2 (a( 0; );b( 0; )(a38a176 t0 2 ( ; ). a108a94a107
16、a225 a234 a182a94a102a44a11 (t0; 0; 0)a41a94a88 (t0; 0; )a172a37 S a5a42a60a63a24a64 a237a81a24a214a40a24a219a199a145a225a58a60a87a220a3a108a3a109a24a236a3a110a98 a41a24a71a24a72a24a73dxdt = f(t;x; ); (E) a32a5 a81 m a111a40a97a42a98a24a60a80a68a237a3a112a110a1a64a34a66a34a41 , (E) a217a24a81a17a113
17、a62a114a108a3a109a188a34a41a34a71a24a72a34a73a34a60a75a115a34a81a103a110a98 a111a118a211a118a105a118a47 a71a118a72a34a73 (E) a41a44a42a44a116a118a223a118a224a24a111a24a190a24a47a99a117a24a170a34a41a24a77a1a37a24a87a3a118a1a119a24a223a34a224a24a111a34a190a24a60a109a205 (E) a41a118a77a118a102a44a101a4
18、4a120 a41a118a111a118a190a118a79a118a111a24a190a34a47 a108a24a110a40a106a42a107a34a37a24a170a34a171a95a37a173a119a174a24a175a34a176a24a177a60 a252a90a24a37a40a239a42a181a24a182a34a71a34a72a153a212a34a183a34a184a153a41a34a215a122a121a1a123a1a124a125a5a58a47a110a98 a33a3a33a3a47a3a126a24a185a34a186a1a
19、127a34a46a122a128a1a129a150a252a71a130a153a41a1a131a132a47 a79a118a108a118a186a44a131a132a44a133a3a133a3a134a169a3a12a24a201a24a194a24a52a24a193a24a98a40a233a62a35a24a60a35a102a110a98 a41a118a181a118a202a118a203a118a204a118a207a118a208a24a68a24a170a24a77a41a44a36a44a135a118a111a118a190a118a47 a92a24
20、a93a24a212a24a213a24a214a34a41a24a77a24a217a24a195a24a196a3a11a3a27a24a52a24a183a24a184a34a212a108a3a109a41a3a136a3a137a24a47 a252a42a79a1a37a24a217a3a138a173a3a139a210a24a216a24a75a24a60a36 Ga90 (t;x) a38a40a39a24a44a42a185a24a43a24a47 D a90 a38a40a39a24a44a42a185a24a43a24a60a35a24a36 f(t;x; )a37G
21、D : (t;x) 2G; 2Da44a49a45a118a46a118a47 a48a118a68 (x; ) a53a118a54a118a55a161a56a49a57a118a59a24a60a237a81a24a61a34a62a24a78a24a37a24a247a24a82a34a70a3a65a24a66a24a67a24a47 a68a112a70 2D,a71a118a72a118a73 (E) a41a118a77a172a239a49a74a118a75 ( ; ) a82a118a70a118a194a118a66a118a60 a108a24a77a24a170a2
22、4a89a34a90 x = (t; ; ; ). a65a44a140a220a70a3a23a24a47a80a83a24a85a35a24a36a108a24a110a24a77a34a81a24a76a34a65a24a41a34a60a112a24a113 6.2a114 f(t;x; ) a115a34a120 G D a121a58a122a34a123a34a47a80a124a34a166 (x; ) a126a34a127a153a128a34a129a34a130a34a131a145a132a34a133a134a118a60a135 x = (t)a136 (E) 0
23、; 0 2D a119a49a137a118a138a118a139a118a47 t a136a118a141a118a142a118a143a161a144a24a117a34a119a42a146a24a137a34a147a148a40a149a42a151a40a144a24a117a42a47a153a152a42a142a24a143 0, a154a24a155 x = (t; ; ; ) a115a40a149a42a120V : t ; ; j ( )j + j 0j 4a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a
24、13a14a15a17a16a14a18a14a19a14a20a162a24a147a24a163a24a164a24a124a24a122a24a123a24a60a141a3a142a255a3a143a24a87a24a66a24a67 6.1 a171a237a71a24a72a24a7380, a103 k a234a24a182a24a210a3a30 x = (t; ; k) a237 t a173 a66a177a47a80a48j(t; ; k) (t)j 0a4a118a214a161a235a49a43 U : t ;jx (t)j a236a118a237 G a44
25、a49a60a180a89 M a90jf(t;x)ja237 U a41a118a70a118a110a95a118a245a60 a231a24a199a40a225a42a103 ka234a118a182a118a210a44a30 (t; ; k) a227a237 t + 4Ma95a118a173a66a177a47a187a148a24a199a145a225a237a254a145a91a24a39 f(t; ; k)ga70a44a18a44a59a44a60a237 (t).a228a44a119a118a37 + 4M t + 2 4M a95 a89a3a90a24a
26、602. a36 f(t;x) a81a34a104a253a98a34a99a34a100a34a47a237 (t;x)a229a220a45a34a46a34a86a34a181a34a47a80a48a34a78a153a37a153a251a34a100 A, a4a34a214a34a103jxj Aa105a24a47 xf(t;x) 0. a199a40a225a62a227a173a88 (0; ), a4a24a214a24a71a24a72x0 = f(t;x)a188a24a254a3a88a24a41a24a77 x = (t;0; ) a237 1t +1a95a2
27、4a173 a66a177a60a225a44a226a229a99a38a176a44a40a103 j j Aa105a118a47 (t;0; ) a227a237 1t 0 a173a66a177a47 a252a49a254a24a255a1a143a230a53a118a54 j j Aa41 , a4a118a214 (t;0; ) a37a237 0 t +1a95a118a173a66a177a60 a171a3a231a24a199a3a12a24a60a232a222a24a53a54 j j Aa41 ;x = (t;0; ) a172 a195a24a196a24a37 0 t +1 a95a24a173 a66a177a47a224 x = (t;0;A)a227a118a247a44a233a118a243 x = A+ 1 a117a44a234a118a47 x = (t;0; A) a227a118a247a44a233a118a243 x = A 1 a117a44a234a118a60a99a147a44a235a24a182a12a3a95a24a67a40a91a24a39 j j A, a45a24a86a63a233a62a236a3a237a24a606
