1、a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a3a14a5a14a6a14a7a20 1a21a23a22a24a23a25a27a26a23a28a23a29a23a30a23a31a23a32a23a33 ,a34a23a35a23a36F(x1; ;xn;u; ux1; ; uxn) = 0; (1.1)a37a39a38 x1; ;xn a36a41a40a43a42a23a44a23a45 ua36 x1; ;xn a35a23a46a23a47a23a48a23a4
2、9a23a50a51a53a52a53a54 (x1; ;xn) a55a57a56a59a58a53a60 D a61a59a35a53a48a53a49 u = (x1; ;xn) a62a53a63a53a64a53a65 (1.1)a54a60 D a61a66a35a68a67 , a69a71a70a71a72a54a60 D a61a66a73a71a74a71a75a71a76a71a77a78a49a79a45a81a80a79a82a79a83a78a84 (1.1) a85a71a86a71a87a71a35a71a36a74a71a88a54 Da61a66a89a71
3、a90a71a35a71a91a71a92a79a93a79a50a81a64a78a65 (1.1) a35a71a94 u = (x1; ;xn) a95a71a96a71a97a71a89a71a83a71a98(x1; ;xn;u) a55a39a56a38a35a23a74a23a88a39a99a101a100a23a45a79a102a66a103a71a104a71a62a23a63a71a64a23a65 (1.1) a35a27a105a31a39a106a101a107 .a108a74a53a75a53a76a53a109a53a110a53a64a53a65a53a1
4、11a23a112a23a73a53a113a23a35a51a94a57a114a101a115a23a36a23a116a53a117a39a114a101a115a23a50a119a118a23a120a23a74a23a75a53a121a23a122a23a123a23a76a53a109a23a110a64a23a65ux1 = f(x1; ;xn;u;ux2; ;uxn );a37a116a23a117a39a114a101a115a23a36a23a124a126a125a23a72a23a127a71a128a23a116a71a117a23a129a71a130ujx1=
5、x01 = (x2; ;xn)a35a23a94a23a45a37a39a38 x01 a36 x1 a35a23a74a23a131a51a117a23a45 (x2; ;xn) a36 x2; ;xn a35a39a132a101a47a23a48a23a49a23a50a133a23a134a23a135a23a136a123a23a69nXi=1ai(x1; ;xn;u)uxi= c(x1; ;xn;u) (1.2)a35a23a64a23a65a23a45a126a72a23a62a23a63a26a23a28a23a137a23a138a23a139a23a32a23a33 .a6
6、9a23a70a23a48a23a49 aia140a23a141a23a142a23a143a120 u, a144a23a123a23a69nXi=1ai(x1; ;xn) uxi= c(x1; ;xn;u) (1.3)a35a23a64a23a65a23a62a23a63a146a145a138a23a139a23a32a23a33 .a69a23a70 ca118 ua147a23a36a23a148a23a149a23a35a23a45a126a150a23a64a23a65 (1.3) a62a23a63a138a23a139a23a32a23a33 .a54a113a53a120
7、a53a74a53a75a53a76a53a109a23a110a71a64a23a65a23a35a23a151a23a152a38a45a153a111a23a154a23a35a23a155a23a156a23a36a71a157a23a158a133a23a159a157a23a160a23a161a23a35a23a50a153a162a23a163a23a164a51 a1; ;an a141a39a165a101a166a63a23a167a23a50a126a168a166a64a170a169(a1(x1; ;xn); ;an(x1; ;xn)a62a23a63a23a64a
8、23a65 (1.3) a54a23a171 (x1; ;xn) a172a23a35a174a173a23a175a32a23a176 .a48a23a49 ua177a23a178a23a168a23a88a23a64a39a169a101a35a23a64a39a169a101a77a49a23a179a23a36nXi=1uxi ai(a21 + +a2n)1=2 =1(a21 + +a2n)1=2 nXi=1ai uxi:1a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14
9、a3a14a5a14a6a14a7a180x1 = x1(t); ;xn = xn(t) (1.4)a36a23a64a23a65a23a181 8:dx1dt = a1(x1; ;xn);dxndt = an(x1; ;xn)(1.5)a35a23a94a23a50a126a150ddtu(x1(t); ;xn(t) =nXi=1uxi dxidt =nXi=1ai uxi:a182a23a183 u = u(x1; ;xn) a36a23a64a23a65 (1.3) a35a23a94a23a45a126a150a23a72a23a177a23a178 (1.4) a184a23a89a
10、23a185a23a186a23a109a23a110a23a64a23a65a23a124dudt = c(x1(t); ;xn(t);u):a186a23a109a23a110a23a64a23a65a23a181 (1.5) a62a23a63a23a64a23a65 (1.3) a35a174a173a23a175a32a23a33a23a187 , a37a94 (1.4)a54 (x1; ;xn) a55a56a101a35a39a188a101a189a23a62a23a63a23a64a23a65 (1.3) a35a190a173a23a175 . a186a23a109a2
11、3a110a23a64a23a65a23a1818:dx1dt = a1(x1; ;xn);dxndt = an(x1; ;xn);dudt = c(x1; ;xn;u)a62a79a63a79a64a79a65 (1.3) a35a192a191a79a173a79a175a32a79a33a79a187 , a37a94a54 (x1; ;xn;u) a55a193a56a126a35a193a188a126a189a79a62a79a63a78a64a78a65(1.3) a35a190a191a23a173a23a175 .a118a53a120a53a64a53a65 (1.2),
12、a95a53a194a53a195a53a196a53a197a23a35a23a155a71a156a23a50a198a164a51 a1; ;an a141a39a165a59a166a63a53a167a53a50a199a118a23a131a51a35a58a23a74a23a48a23a49u = u(x1; ;xn); (1.6)a64a39a169(a1(x1; ;xn;u); ;an(x1; ;xn;u)a62a23a63a23a64a23a65 (1.2) a54a23a171 (x1; ;xn) a172a201a200a23a202a23a203a23a173a23a
13、204a71a205a79a206 (1.6) a207a23a173a23a175a32a23a176 .a186a23a109a23a110a64a23a65a23a181 8:dx1dt = a1(x1; ;xn;u(x1; ;xn);dxndt = an(x1; ;xn;u(x1; ;xn)2a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a3a14a5a14a6a14a7a62a23a63a23a64a23a65 (1.2)a200a23a202a23a203a23a17
14、3a23a204a23a205a23a206 (1.6) a207a23a173a23a175a32a23a33a23a187 , a37a94a54 (x1; ;xn) a55a39a56a101a35a188a101a189a23a62a23a63a23a64a23a65 (1.2)a200a23a202a23a203a23a173a23a204a23a205a23a206 (1.6) a207a23a173a23a175 . a186a23a109a23a110a23a64a23a65a23a1818:dx1dt = a1(x1; ;xn;u);.dxndt = an(x1; ;xn;u
15、);dudt = c(x1; ;xn;u)(1.7)a62a79a63a79a64a79a65 (1.2) a35a192a191a79a173a79a175a32a79a33a79a187 , a37a94a54 (x1; ;xn;u) a55a193a56a126a35a193a188a126a189a79a62a79a63a78a64a78a65(1.2) a35a190a191a23a173a23a175 .a208a111a53a154a53a64a53a65a53a181 (1.7) a108 a64a53a65 (1.2) a35a53a160a53a161a53a209a53a
16、210a54a120a23a124a211a64a23a65 (1.2) a35a53a212a53a110a57a99a59a100a57a213a72a23a35a208a111a23a154a23a214a39a215a101a45a126a144a23a162a71a163a23a73a71a216a23a100a71a35a51a23a217a50a204a23a218 1.1 a219 ai(x1; ;xn;u);i = 1; ;na220 c(x1; ;xn;u) a221a53a222 (x1, ,xn;u) a223a23a224a23a225a101a226 G a227a
17、101a228a23a229a23a230a23a231a23a45a126a232a23a233u = (x1; ;xn) (1.8)a222 (x1; ;xn) a223a53a224a53a225a59a226 D a227a59a228a53a229a53a230a53a231a23a45a235a234 (x1; ;xn; (x1; ;xn) 2 G. a236a237a23a238 (1.8)a239a23a240a23a241 (1.2) a225a101a242a23a243a237a23a238a225a23a244a101a245a39a246a101a247a71a239
18、a23a124a81a248a71a249a71a250a23a251a71a252a23a253a170a225a66a254a23a255a1a0a1a2a4a3a5a4a6a253a4a7a4a8a39a225a101a252a4a9a4a10a23a222a23a249a71a250a71a50a11a4a12 a13a4a14a4a15a110a23a149a23a50a180 (x01; ;x0n;u0)a36a39a99a101a100 (1.8) a104a4a16a4a17a23a74a171a45a19a18x1 = x1(t); ;xn = xn(t); u = u(t)
19、 (1.9)a36a23a64a23a65 (1.2) a54 t = a166a4a20a4a21a171a35a208a111a23a154a23a50a19a22 jt j ha166a73u(t) (x1(t); ;xn(t):a118 ta125a23a77a23a45a79a213 (1.7) a86c(x1(t); ;xn(t);u(t)du(t)dt d dt (x1(t); ;xn(t)nXi=1ai(x1(t); ;xn(t);u(t) xi(x1(t); ;xn(t):a111a23a112a4a22 t = a166a73c(x01; ;x0n;u0) =nXi=1ai
20、(x01; ;x0n;u0) xi(x01; ;x0n):3a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a3a14a5a14a6a14a7a213 (x01; ;x0n;u0) a35a4a16a4a17a23a149a23a144a23a47 (1.8) a36a23a64a23a65 (1.2) a35a23a212a23a110a39a99a101a100a23a50a23 a14a4a24a161a23a149a23a50a180 (1.8)a36a23a64a23a6
21、5 (1.2) a35a23a212a23a110a39a99a101a100a23a45 (x01; ;x0n;u0) a36a37a104a4a16a17a23a74a171a45a19a18 (1.9) a36a23a64a23a65 (1.2) a54 t = a166a4a20a4a21a171a35a208a111a71a154a71a45a26a25a54a120 jt j ha104a23a50a19a27a4a28a23a48a23a49a23a181x1 = 1(t); ;xn = n(t); u = (t); (1.10)a37a39a38 x1 = 1(t); ;xn
22、= n(t) a36a23a64a23a65 (1.2)a54 t = a166a4a20a171 (x01; ;x0n) a35a4a29a30a120a23a111a51a48a23a49 (1.8) a35a23a111a23a154a23a45a126a144a23a64a23a65a23a1818:dx1dt = a1(x1; ;xn; (x1; ;xn);.dxndt = an(x1; ;xn; (x1; ;xn)a127a23a128a23a116a23a117a23a129a23a130x1( ) = x01; ;xn( ) = x0na35a23a94a23a45a141a4
23、a31a180a72a4a32a4a25a54a120 jt j ha104a23a45a19a18(t) (1(t); ;n(t): (1.11)a33a161 ha34a4a22a4a35a23a45a126a179a23a73(1(t); ;n(t); (t) 2 G; jt j h:a36a18a23a73d (t)dt nXi=1ai(1(t); ;n(t); (t) xi(1(t); ;n(t)c(1(t); ;n(t); (t):a168a38a37a40a39 (1.10) a32a53a36a208a111a53a154a53a64a23a65a23a181 (1.7) a3
24、5a53a94a53a45 a80a53a82a54 t = a166a32a38a41a20(x01; , x0n,u0). a213a101a64a23a65a23a181 (1.7) a35a23a116a23a117a39a114a101a115a23a94a23a35a4a42a23a74a23a149a71a45a81a73x1(t) 1(t); ;xn(t) n(t); u(t) (t):a213a21a4a43(1.11) a86a23a87u(t) (x1(t); ;xn(t); jt j h;a168a23a179a23a36a24a161a14a39a101a35a23a
25、50 4a0a2a1a4a3a4a5a4a6a4a7a4a8a4a9a4a10a4a11a4a7 a12a14a13a14a15a17a16a14a18a14a19a14a3a14a5a14a6a14a7a54a96a23a216a23a35a135a23a136a39a38a45a126a162a23a163a71a147a71a161a4a44a43a1a45a94a71a35a71a155a23a156a71a50a81a74a71a88a23a74a71a75a71a76a23a109a71a110a71a64a23a65a71a35a47a46a23a67 ,a162a53a163a
26、38a48a217a94a53a63a38a49a23a58a1a50a4a16a4a17a4a51a4a52a23a35a23a94a23a35a23a98a4a53a23a93a71a50a54a22a4a34a4a22a4a55a4a56a24a49a4a16a4a17a1a51a4a52a166a45a54a57a23a88a112a4a58a4a59a23a45a126a95a23a96a23a86a23a87a23a64a23a65a71a35a4a16a71a74a23a94a71a50a81a97a71a216a23a100a71a35a1a58a4a60a71a50a61 1
27、.1 a180a40a43a42a23a44a23a36 x;y, a46a23a47a23a48a23a49a23a36 u. a150a23a64a23a65uy = 0a35a45a94a23a36 u = !(x),a21a172 !(x) a36 xa35a4a16a4a17a23a48a23a49a23a50a61 1.2a64a23a65ux uy = 0a41a23a42a23a44a23a42a4a62x+y = ; x y = ; u(x;y) = v( ; )a179a23a184a23a892v = 0:a63a21a4a45a94a23a63 v = !( ), a144u = !(x+y);a37a39a38 !a36a4a16a4a17a23a95a23a109a23a48a23a49a23a50a64 a65a132a101a47 x;y a36a41a40a43a42a23a44a23a45 ua36a23a46a23a47a23a48a23a49a23a45a126a94a23a216a4a66a23a64a71a65a23a124(1) ux + uy = 0;(2) ux + uy = 0, a37a39a38 a159 a36a4a67a23a88a141a208a63a23a167a23a35a4a68a23a49a23a505
