WWW.DISSERS.RU


...
    !

e P PE E E E E E E Paccop oe, e epeee ec e oo o pee, o pocpace. B oe o oex ae oe aac pacpeee ( pocpace). B pacpeeex cceax oy poea oex oax pocpaca xece pepae eec oopeeo pocxo y oex eec eeapx oeo c coo oepae oe c ee oepae. Ta opao, c ey coce eeap oea ocyecec a ce poecco epeoca. B ooecx cceax (ae epa, a, cooeca opao) ae cyecy pacpeeee co ep. ac o ep ccpye eeapx oeax cce. Tae cce oocc a pacpeee ccea.

pepo ooecoo poecca, poeaeo pacpeeeo ccee, cy opaoae cpyyp opoeee. Oo pocxo e a ce ex oo, a caopooo a ocoe opa, aeo oooopeo eee, cxoo pocpaceo oopoo cpee. Pe e ao cyae o ooe ao pacpeeeo ccee caoapx pocpaceo eoopox cpyyp. pyo pep pacpocpaee o oye epo eo a.

cceoae pocex oee oaao, o pae oee ax pacpeeex cce oy oca ee epea ypae acx poox, e yac xece pea y peaeo.

46 Pcyo. 4.1 Pacpeeea ccea c oo epeeo x, yacye xeco poecce ypye o yo py Paccop poce cya oo epeeo x, oopa yacye xeco poecce oopeeo ypye o yo py (pc. 4.1). y oo eeca (. e. acca, poxoa ey pee epe ey oa, epeypo apae y) poopoae paey oepa oo eeca, oy c opa ao c(r,t) I =-D, (4.1) r e D oe y.

Moo oaa, o eee oepa eeca o pee a ce poecco y eeapo oee py, aeo ey oa r r+r, ac o paoc ooo I oax r r+r peee p r 0 pao c I c(r,t) =- = D t r r r Ec oe y D ocoe, o ypaee y ee c c(r,t) = D. (4.2) t rpaee (4.2) ocae eee o pee oepa eeca, oa ccee pocxo oo y. Oao poe y pocxo xece pea, oop pocee f (c) cyae cooecy "oee" e. Oee ypaee ee "c" a ce xeco pea y ee c c = f (c) D. (4.3) t rc1,c2,...,cn, Ec ccee eec ecoo eec o eco (4.3) ao aca ci ci = fi (c1,c2,...cn ) Di, i = 12,...,n. (4.4), t r pecae coo pyy aay, a oopo ocaoc cax ox epax. pee cce ooex epeax ypae (oex oee) eoxoo o aa aae ae epeex aa oe pee t = t. B cyae pacpeeex cce ceye aa ae paee pae yco a pae oac, peeax oopo poeae yae poecc.

paee yco ac o oo, a opao ec oepa eeca a pae. Hapep, a pa py oe aaa ocoa oepa eeca peepyape, c oop pya axoc oae, , aoopo, op py epoae yooo ooa.

ae, o pacpeeey ccey (4.4) oo cec oeo ci = f (c1,c2,...cn); i = 12,...,n.

, t ec ce oe y D = 0 ec, aoopo, o oe i e, a o ce cxoe peae poy ycea ooc epeeac o ce peaoo oee o pe xeco pea. Caoape o ao ca yco paeca y ci poox o pee = 0:

t c(r,t) Di fi (c1,c2,..., cn ) = 0, (4.5) M rc oya oo a caoape ae (r). ae aaec eoi opoe oyee c (r) cceyec oeee eo o pee. Ec i co peee p t eceoe eooe oyee c (r) e apaci c ae ccee, o cxoa caoapa oa (r) a ycoo.

i oeee aaoo ooe ac o coc y f (c,c,...,c ) ae oeo y. B acoc, oi 1 2 n fc c oepo aa p ( )<0 aaoe ooee co peee ye ayxa p t (aa 1, cp. 1315).

p oo ooo ypae e oca cooe oeee epeex, apep oeaeoe cocoe cce. Ocoe peya cceoa coc pacpeeex cce oye a a aaex aox oex c y epee (cp. (2.1)):

x x = P(x, y) Dx, t ry y = Q(x, y) Dy. (4.6) t rOaaoc, o a poca oe a (4.6) oe aeceo oca poecc caopoooo ooe o cpyyp pacpeeex cceax, . e. poecc caoopaa. O ocyecc, oa ccee oa eycooc, poe oepe cxooo pacpeee eec o pee pocpace. Beco oo ycaaaec o pacpeee eeca o pee pocpace, . e. pocxo caoopaa cce. Hapep, oep ycooc caoapoo pocpaceo oopooo pacpeee eec xeco pea oe pec oy, o eco eo ccee oc aoo epoece caooepaec o xeco aoc.

B acoc o a y f (c,c,...,c ) oeo i 1 2 n y D cceax oy oa ceye epae i oee epeex caoopaa.

1. Pacpocpaec oye e eyeo yca.

2. Coe o.

3. Cxpoe aooea pax eeo o ce pocpace.

4. acoxacece o, oope oyac p cyao oye paoc a aooea yx oax pocpaca.

5. Caoape eoopoe pacpeee epeex pocpace ccae cpyyp.

6. eepa o aoo coa yco aoc. B aece coo o oy , apep, oae paopeee yya epeex.

O ycoe pa poecco caoopaa ec oee eycooc cxoo pacpeeeo ccee. B acoc, oee eycooc a cea ae oee ccax cpyyp, a oee eycooo ya oe a ooee eyx o oeo ay cox o.

ccaa cpyypa, oaa peyae eycooc pacpeeeo ccee, oepaec a ce ocooo poa ep eeca oe aac oo opx cceax. B o ee oe o ox paoecx cpyyp. Opaoae aoo poa ccax cpyyp e ocoe epepo ae p opoeee. Caoopa epexo ey cca cpyypa pao op, oop ypyec p yee peaooo cocya, opaae pay ocoeoc poecca ee e.

pecae coo aoee cceoay ccey, oopa p pax aex apaepo oe oaa paoopa oeee o pee pocpace. Ha oe pcceopa yaec yco ooe o caoopaa ooecx xecx cceax, o cce a oe ec aoo. Opa ae a o, o pcceope coepc pocea yeca eeoc, oopa oeceaec peae 2x + y 3x pepo ao pea oe epea poecc, oopo epe ee o pae epe p aaecx epa. yeca eeoc aoe ycoe ooe ccax cpyyp.

pcceop pecae coo ceyy cxey oeecx xecx pea:

A x, 2x y 3x, (4.7) B x y C, x R, e A, B cxoo aae eeca, pacpeeee pye paoepo, x aac e; eeca R C aa e ocaa. epeee x y ypy o py yacy xeco poecce.

Moe pcceopa ee x = A x2 y - (B 1)x Dx x, t r(4.8) y y = Bx - x2 y Dy.

t rpee peya cceoa o oee oe (4.8) acoc o coooe apaepo (A, B, D, D ). Toea oe x y (D =D =0) oaae caoapo oo x y x = A, y = B / A. (4.9) p B<1+A2 a oa pecae coo yco oyc, a p B>1+A2 eyco oyc, opy oopoo oeo ccee opayec pee .

B pacpeeeo ccee (4.8) ooo oee eycooc ceooo a, oopa po pa oye pocpaceo oopoo ccee ycaoe e pocpaceo eoopox caoapx peo. p opeeex paepax py ax o, opeex xapaep eoopooce peaoc pocpaca, ccee ooo ooee epoecx ccax cpyyp, e acx o pee. x oe eoxoo, o oe D D x y cyeceo pa, a apaep A B e co ae o cox ypaox ae. poe oo, pcceope oo ae aoooe poecc a coe eye o. Hepepoe eee apaepo po oy, o o ccae cpyyp ce pye. Ta opao, pcceop ec pacpeee pepo co o yco coco opa ccax cpyyp.

Ha ocoa aoo oe poecc ee e oo ca c apaepec aa opaoae oo ccao cpyyp, opaee oopo eooo cy cepeca.

oop, o opaoae ccax cpyyp opeeec aec cae apaepec aao opa.

Booe poecc oo aa px cepeax a pepe oceo occaoeo pea eoycoaaocoo c yace poaooo co c aaaopa oa ep apaa. poecc ae ocac ypae aooo a (4.8) He (e 5) paccop oe opaoa ccax cpyyp ooecx cceax.




2011 www.dissers.ru -

, .
, , , , 1-2 .