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Усереднення нелінійних крайових задач в областях з тонкими порожнинами: Автореф. дис… д-ра фіз.-мат. наук / М.А. Наумова, НАН України. Ін-т приклад.

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee

Iaoiiaa Ia?eia Aiaoie??aia

OAeE 517.956

ONA?AAeIAIIss IAE?I?EIEO E?AEIAEO CAAeA*

A IAEANOssO C OIIEEIE II?IAEIEIAIE

01.01.02 — aeeoa?aioe?aeuei? ??aiyiiy

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Aeiiaoeuee — 1999

Aeena?oaoei?th ? ?oeiien.

?iaioa aeeiiaia a Aeiiaoeueeiio aea?aeaaiiio oiiaa?neoaoi, I?i?noa?noai
ina?oe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?, aeaaeai?e
IAI Oe?a?ie Ne?eiiee ?ai? Aieiaeeie?iae/, ?inoeooo i?eeeaaeii?
iaoaiaoeee ? iaoai?ee IAI Oe?a?ie, aee?aeoi?.

Ioioeieii iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Aacae?e
Ai?en Aaneeueiae/, ?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI
Oe?a?ie, caa?aeoaa/ a?aeae?eii ??aiyiue iaoaiaoe/ii? o?ceee;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, Iaie?aoia Eaii?ae Na?a?eiae/,
O?ceei-oaoi?/iee ?inoeooo iecueeeo oaiia?aoo? ?i. A.?. A??e?ia IAI
Oe?a?ie, noa?oee iaoeiaee ni?a?ia?oiee.

I?iaiaeia onoaiiaa: ?inoeooo iaoaiaoeee IAI Oe?a?ie, i. Ee?a, a?aeae?e
??aiyiue c /anoeiieie iio?aeieie.

Caoeno aeena?oaoei? aiaeaoaeaoueny «19» eenoiiaaea 1999 ?ieo i 15.00
aiaeeii ia caniaeaiii niaoeiaeiciaaii? a/aii? ?aaee Ae 11.193.01 i?e
?inoeooo? i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith:

340114, i. Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74.

C aeena?oaoei?th iiaeia iciaeiieoenue o a?ae?ioaoe? ?inoeoooo
i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith:

340114, i. Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74.

Aaoi?aoa?ao ?iciceaiee «13» aeiaoiy 1999 ?ieo.

A/aiee nae?aoa? niaoeiaeiciaaii? a/aii? ?aaee ____________________
Eiaaeaanueeee I.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. ??ciiiai?oi? caaea/? a?ae?iaeeiai?ee, oai???
i?oaeiino? oa ?ioeo ?icae?e?a o?ceee oa iaoai?ee i?eaiaeyoue aei
iaiao?aeiino? aea/aiiy neeueii iaiaeii??aeieo na?aaeiaeu oa o?ce/ieo
i?ioean?a, ye? a ieo i?io?eathoue. Iaoaiaoe/iee iien oaeeo na?aaeiaeu oa
i?ioean?a caiaeeoueny aei aeaio i?iaeai: ona?aaeiaiiy e?aeiaeo caaea/
aeey aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie iio?aeieie, ui iathoue
oaeaeeieieeai? eiao?oe??ioe oa ona?aaeiaiiy aeeoa?aioe?aeueieo
iia?aoi??a a iaeanoyo neeaaeii? no?oeoo?e. Aieiaiith iaoith oeeo caaea/
? iiaoaeiaa ona?aaeiaieo caaea/ aeey ??aiyiiy c i?inoeie eiao?oe??ioaie,
aai a i?ino?e iaeano?, aei ?ica’yce?a yeeo ca?aathoueny (i?e iaaieo
oiiaao) ?ica’ycee ii/aoeiaeo caaea/.

Ieoaiiy ona?aaeiaiiy e?aeiaeo caaea/ a iaeanoyo neeaaeii? no?oeoo?e
aia?oa aoee ?icaeyioo? a 60-o? ?iee a ?iaioao A.I. Ia?/aiea oa ?.ss.
O?oneiaa. Aiie ?icaeyaeaee e?i?ei? e?aeia? caaea/? a ia?oi?iaaieo
iaeanoyo, ye? iaea?aeai? ?c o?eniaaii? iaeano? oeyoii aeeeaeaiiy aaeeei?
e?eueeino? ae??aieo eiiiiiaio, ye? ia ia?aoeiathoueny.

A na?aaeei? 70-o ?ie?a c’yaeeenue ia?o? ?acoeueoaoe c ona?aaeiaiiy
e?aeiaeo caaea/ aeey ??aiyiue c ia??iaee/ieie oaeaeeieieeaieie
eiao?oe??ioaie a ?iaioao A. Aea Aeaei?aeae? oa N. Niaiueiei, A.
Nai/an-Iaeain?y, A. Aainonnaia, AE.-E. E?iina oa Aeae. Iaiai?eieao, I.N.
Aaoaaeiaa, I.A. Ie?eiee.

A iiaeaeueoiio oai??y ona?aaeiaiiy iaaoea ?ioaineaiiai ?icaeoeo a
?iaioao aaaaoueio iaoaiaoee?a, ianaiia?aae, ?.ss. O?oneiaa, I.N.
Aaoaaeiaa, I.A. Ie?eiee, N.I. Eiceiaa, ?.A. Ne?eiieea, A.A. AEeeiaa,
A.A. Iaieiaa, Aeae. Aeaeue Iaci, O. Ith?a, E. Nai?aeiia, A.
Nai/an-Iaeain?y oa ?i.

C i?iaeaiaie ona?aaeiaiiy e?aeiaeo caaea/ c /anoeiieie iio?aeieie o?nii
iia’ycaia oai??y G-ca?aeiino? iia?aoi??a oa A-ca?aeiino? ooieoe?iiae?a.
Aea/aiith ieoaiue oe??? oai??? i?enay/ai? ?iaioe oaeeo iaoaiaoee?a, ye
A. Aea Aeaei?aeae?, N. Niaiueiei, O. O?aicii?, A.A. Iaieiaa, I.A.
Ie?eiee, N.I. Eiceiaa oa aaaaoueio ?ioeo. Ieoaiiyi G-ca?aeiino?,
A-ca?aeiino? oa ona?aaeiaiiy aeey iae?i?eieo ae?ioe/ieo iia?aoi??a oa
?ioaa?aeueieo ooieoe?iiae?a c? ci?iiith iaeanoth aecia/aiiy i?enay/ai?
?iaioe A.A. Eiaaeaanueeiai.

Nooo?aiai ?icaeoeo iaaoei ieoaiiy ona?aaeiaiiy e?aeiaeo caaea/ a ci?iieo
iaeanoyo a ?iaioao ?.ss. O?oneiaa. A?i ?ic?iaea aa??aoe?ei? iaoiaee
aeine?aeaeaiiy aneiioioe/ii? iiaaae?iee ?ica’yce?a caaea/ Ae???oea oa
Iaeiaia aeey e?i?eieo ??aiyiue a ia?oi?iaaieo iaeanoyo iaia??iaee/ii?
no?oeoo?e, io?eiaa aeinoaoi?, a a aeayeeo aeiaaeeao ? iaiao?aei?, oiiae
ca?aeiino? ?ica’yce?a caaea/, ye? ?icaeyaeathoueny, aei ?ica’yce?a
ona?aaeiaieo caaea/ o oa?i?iao ca?aeiino? niaoe?aeueieo /eneiaeo
oa?aeoa?enoee ia?oi?iaaieo iaeanoae. Iaoiaee, ye? cai?iiiioaaa ?.ss.
O?oneia, aoee ?icaeiai? o ?iaioao E.N. Iaie?aoiaa, E.A. Aa?eyiaea, ?.TH.
*oae?iiae/a, ?.A. Na?uaai?, oa ?ioeo.

Caaea/? Ae???oea aeey iae?i?eieo ??aiyiue ae?oaiai ii?yaeeo a iaeanoyo
neeaaeii? iaia??iaee/ii? no?oeoo?e aia?oa aoee aeine?aeaeai? ?.A.
Ne?eiieeii. Iei aoee ?ic?iaeai? iaoiaee ona?aaeiaiiy caaea/ Ae???oea
aeey eaac?e?i?eieo ae?ioe/ieo ??aiyiue a iine?aeiaiino? ia?oi?iaaieo
iaeanoae oa aea/ai? oe? caaea/? o aeiaaeeao ia’?iiiai oa iiaa?oiaaiai
?iciiae?eo «ca?ai». Nooue oeeo iaoiae?a iieyaa? a iiaoaeia?
aneiioioe/iiai ?iceeaaeo iine?aeiaiino? ?ica’yce?a caaea/, ye?
?icaeyaeathoueny, aea/aii? iiaaae?iee /eai?a oeueiai ?iceeaaeo.
Aeei?enoiaoth/e aneiioioe/iee ?iceeaae, onoaiiaeththoue aeinoaoi? oiiae
ca?aeiino? iine?aeiaiino? ?ica’yce?a caaea/ a ia?oi?iaaieo iaeanoyo oa
aoaeothoue ona?aaeiaio caaea/o aeey a?aie/ii? ooieoe??. Aeine?aeaeaiiy
/eai?a aneiioioe/iiai ?iceeaaeo oa aeaaaeaiiy a?aie/iiai ??aiyiiy
aaco?oueny ia iioi/eiaeo oa ?ioaa?aeueieo ioe?ieao ?ica’yce?a
niaoe?aeueieo iiaeaeueieo iae?i?eieo caaea/, io?eiaieo ?.A. Ne?eiieeii.
Iiaeaeueoiai ?icaeoeo oe? iaoiaee iaaoee a ?iaioao ?.A. Ne?eiieea, A.?.
I?ieiiaiei, ?.?. Ne?eiieea, Ae.A. Ea??ia.

Iaoiaee, cai?iiiiiaai? aeey aea/aiiy iae?i?eieo ae?ioe/ieo caaea/
Ae???oea a ia?oi?iaaieo iaeanoyo, aoee aeei?enoai? i?e aea/aii?
ona?aaeiaiiy iae?i?eieo ia?aaie?/ieo caaea/ a ia?oi?iaaieo iaeanoyo a
?iaioao ?.A. Ne?eiieea oa N.A. Eaiiiiaa.

Aei inoaiiueiai /ano ona?aaeiaiiy iae?i?eieo caaea/ Ae???oea iaea?eueo
aeaoaeueii aoei i?iaaaeaii o aeiaaeeo ii?iaeiei aai iaeiai ae?aiao?o
(iaeano? c ae??aiica?ienoith iaaeath) aai ?icoaoiaaieo a ieieao e?i?e
(iaeano? c eaiaeaie). A?aecia/eii, cie?aia, i?eioeei aaeeoeaiino?
a?aeiinii ?icaeooy iiiaeei ii?iaeiei ia i?aeiiiaeeie, yeee aeiaaaeaii
aoei eeoa aeey oae ia?oi?iaaieo iaeanoae.

Oiio aeooaeueiei aoei aeine?aeaeaiiy caaea/ ona?aaeiaiiy aeey
eaac?e?i?eieo ae?ioe/ieo oa ia?aaie?/ieo ??aiyiue ae?oaiai ii?yaeeo a
iine?aeiaiino? a?eueo caaaeueieo iaeanoae c ii?iaeieiaie, noai?aiiy aeey
oaeeo caaea/ iaoiae?a aneiioioe/iiai aiae?co.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Oaiaoeea
aeena?oaoe?? iia’ycaia c iaoeiaeie aeine?aeaeaiiyie eaoaae?e
aeeoa?aioe?aeueieo ??aiyiue Aeiiaoeueeiai aea?aeaaiiai oi?aa?neoaoo,
aiia aoea aeeiiaia a ?aieao aea?aeaaii? oaie A-97/25 «Iae?i?ei? a?aie/i?
caaea/?».

Iaoa oa caaea/? aeine?aeaeaiiy. Iaoa aeena?oaoe?eii? ?iaioe —
ona?aaeiaiiy iae?i?eieo ae?ioe/ieo oa ia?aaie?/ieo caaea/ Ae???oea a
iaeanoyo c oiieeie ii?iaeieiaie, ye? i?noyoueny a ieieao aeaaeeeo
iiiaiaeae?a ??cii? ?ici??iino?. Aeey aeinyaiaiiy oe??? iaoe iaiao?aeii
?ica’ycaoe oae? caaea/?:

iaea?aeaoe ?ioaa?aeuei? oa iioi/eia? ioe?iee ?ica’yce?a a?aeiia?aeieo
iiaeaeueieo iae?i?eieo ae?ioe/ieo oa ia?aaie?/ieo caaea/;

iiaoaeoaaoe aneiioioe/iee ?iceeaae aeey iine?aeiaiino? ?ica’yce?a
caaea/, ye? ?icaeyaeathoueny oa aeiaanoe ca?aei?noue on?o eiai /eai?a;

c’ynoaaoe oiiae, i?e yeeo ?niothoue ona?aaeiai? caaea/? o o?eniaai?e
iaeano? oa iiaoaeoaaoe ?o;

aeiaanoe, ui ?ica’ycee ii/aoeiaeo caaea/ ca?aathoueny aei ?ica’yce?a
oeeo ona?aaeiaieo caaea/.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Aia?oa ?icaeyiooi i?iaeaio
ona?aaeiaiiy e?aeiaeo caaea/ aeey iae?i?eieo ae?ioe/ieo oa ia?aaie?/ieo
??aiyiue ae?oaiai ii?yaeeo a iine?aeiaiino? iaeanoae c ii?iaeieiaie, ye?
i?noyoueny a oiieeo ieieao aeaaeeeo iiiaiaeae?a ??cii? ?ici??iino?.
Aea/aii oa?aeoa? ca?aeiino? iine?aeiaiinoae ?ica’yce?a oaeeo caaea/ aei
?ica’yce?a a?aeiia?aeieo ona?aaeiaieo caaea/, iaea?aeai? aeinoaoi? oiiae
ca?aeiino? oeeo iine?aeiaiinoae, iiaoaeiaai? e?aeia? caaea/? aeey
a?aie/ieo ooieoe?e. Aeey oeueiai iiaoaeiaai? aneiioioe/i? ?iceeaaee, a
oiio /ene? ei?aeoi?e aeey iaaeeaeaiiy iine?aeiaiinoae ?ica’yce?a oaeeo
caaea/, anoaiiaeai? oi/i? ioe?iee ?ica’yce?a iiaeaeueieo e?aeiaeo caaea/
aeey iae?i?eieo ae?ioe/ieo oa ia?aaie?/ieo ??aiyiue ae?oaiai ii?yaeeo a
iaeano? c oiieith ii?iaeieiith. I?eioeeiiaei ? anoaiiaeaiiy iaaii?
ca?aeiino? a?aae??io?a ?ica’yce?a, ui ? aaaeeeaei i?e ona?aaeiaii?
iae?i?eieo caaea/ a iaeanoyo c oiieeie ii?iaeieiaie.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Aeena?oaoe?y ia?
oai?aoe/iee oa?aeoa?. ?? ?acoeueoaoe iiaeooue aooe aeei?enoai? aeey
aea/aiiy i?eeeaaeieo o?ceei-iaoai?/ieo i?iaeai, ye? iiaeaeththoueny
iae?i?eieie ae?ioe/ieie oa ia?aaie?/ieie e?aeiaeie caaea/aie a iaeanoyo
neeaaeii? no?oeoo?e.

Iniaenoee aianie aeena?oaioa. ?iaioe [3-6] iaienai? aeena?oaioii a
ni?aaaoi?noa? c iaoeiaei ea??aieeii. Ea??aieeo iaeaaeaoue iinoaiiaea
caaea/? oa iaoiae aeine?aeaeaiiy. Aeena?oaioo iaeaaeaoue anoaiiaeaiiy
oiia aaiiao?e/iiai oa?aeoa?o oa aeiaaaeaiiy iniiaieo ?acoeueoao?a.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. ?acoeueoaoe aeena?oaoe??
aeiiia?aeaeenue oa iaaiai?thaaeenue ia ia’?aeiaiiio nai?ia?? a?aeae?eo
iae?i?eiiai aiae?co oa a?aeae?eo ??aiyiue iaoaiaoe/ii? o?ceee ?III IAI
Oe?a?ie (ea??aieee: aeieoi? o?c.-iao. iaoe, i?ioani?, aeaaeai?e IAI
Oe?a?ie ?.A. Ne?eiiee, aeieoi? o?c.-iao. iaoe, i?ioani? A.A. Aacae?e);
iaoeiaeo nai?ia?ao eaoaae?e aeeoa?aioe?aeueieo ??aiyiue AeiiAeO (caa.
eaoaae?ith: eaiaeeaeao o?c.-iao. iaoe A.E. Iaeueieeia); VIII
?anioae?eainuee?e eiioa?aioe?? «Iaeeiaeiua caaea/e iaoaiaoe/aneie oeceee
e caaea/e ni naiaiaeiie a?aieoeae» (i. Aeiiaoeuee, 1991 ?.).

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a ?iaioao
[1-6].

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?y neeaaea?oueny ?c anooio, o?ueio
?icae?e?a, aeniiae?a e nieneo aeei?enoaieo aeaea?ae. Ianya aeena?oaoe??
— 150 iaoeiiienieo noi??iie, nienie e?oa?aoo?e i?noeoue 103
iaeiaioaaiiy.

iniiaiee ci?no aeena?oaoe??

O anooi? aea?oueny ei?ioeee aiae?c no/aniiai noaio i?iaeaie ?
iaa?oioiao?oueny aeooaeuei?noue oaie, oi?ioeththoueny iaoa oa caaea/?
aeine?aeaeaiiy, iaoeiaa iiaecia, i?aeoe/ia cia/aiiy, ai?iaaoe?y oa
no?oeoo?a ?iaioe.

O ia?oiio ?icae?e? ?icaeyioo? niaoe?aeuei? iiaeaeuei? iae?i?ei? caaea/?
a iaeanoyo c oiieith ii?iaeieiith. Aeey ?ica’yce?a oeeo caaea/ io?eiai?
??ci? ?ioaa?aeuei? oa iioi/eia? ioe?iee.

A i?ae?icae?e? 1.1 aea/a?oueny iiaeaeueia caaea/a Ae???oea aeey
eaac?e?i?eiiai ae?ioe/iiai ??aiyiiy ae?oaiai ii?yaeeo.

oa iicia/eii

. Aoaeaii aea/aoe iiaaae?ieo ?ica’yce?a e?aeiai? caaea/?

, (1)

, (2)

aea F — caieiaia iiiaeeia, yea i?noeoueny a Q’.

oa caaeiaieueiythoue oiiae:

, i=1,…,n;

aeeiiai? ia??aiino?

,

, i=1,…,n

.

— i?ino?? N. E. Niaieaaa ooieoe?e c ii?iith

ioeueia? e?aeia? oiiae.

, eiee, iai?eeeaae, aeiaeaoeiaa oiiaa

aeeiiaia ?ioaa?aeueia oioiaei?noue

.

A oeueiio i?ae?icae?e? aeiaiaeyoueny ?yae iiia?aaei?o ?ioaa?aeueieo oa
iioi/eiaeo ioe?iie, a aeae? iieaco?oueny niin?a iie?auaiiy oeeo ioe?iie,
yeee i?ecaiaeeoue a iiaeaeueoiio aei iniiaiiai ?acoeueoaoo i?ae?icae?eo
— oai?aie 1.

, oaea, ui aeey ?ica’yceo u(x,k) caaea/? (1),(2) a??ia ioe?iea

.

A i?ae?icae?e? 1.2 aeine?aeaeo?oueny niaoe?aeueia iiaeaeueia iae?i?eia
ia?aaie?/ia caaea/a a iaeano? c oiieith ii?iaeieiith.

Iaoae F — caieiaia iiiaeeia, yea i?noeoueny o oeee?iae??

,

. Iicia/eii:

.

Io?eia?ii ioe?ieo ?ica’yceo caaea/?

(3)

(4)

.

— i?aei?ino?? N. E. Niaieaaa ooieoe?e c ii?iith

,

— a?eueaa?oiaee i?ino?? c? neaey?iei aeiaooeii.

oa caaeiaieueiythoue oiiae:

i?e i=1,…,n ;

aeeiiai? ia??aiino?, i=1,…,n.

oa caaeiaieueiy? oiiae:

;

aeeiiai? ia??aiino?.

, c ii?iith.

, ioeueia? e?aeia? oiiae.

aeeiiaia ?ioaa?aeueia oioiaei?noue.

Aeei?enoiaoth/e iaoiae, cai?iiiiiaaiee a i?ae?icae?e? 1.1, aeiaiaeeoueny
ianooiia oai?aia, yea ? iniiaiei ?acoeueoaoii i?ae?icae?eo 1.2.

, oaea, ui aeey ?ica’yceo u(x,t) caaea/? (3),(4) a??ia ioe?iea

.

Iai?ee?ioe? a i?ae?icae?e? 1.3 aea/a?oueny ua iaeia iiaeaeueia
ia?aaie?/ia caaea/a, yea iaiao?aeia aeey aeine?aeaeaiiy ona?aaeiaiiy
n?iaenoaa iae?i?eieo ia?aaie?/ieo e?aeiaeo caaea/.

?icaeyaea?oueny eaac?e?i?eia ia?aaie?/ia caaea/a

, (5)

(6)

, caa??aathoueny an? iicia/aiiy oa oiiae a1), a2), f1), f2), ye?
aaaaeaii? a i?ae?icae?e? 1.2.

Aiaeia?/ii oai?ai? 2, io?eiaia iniiaia ioe?iea ?ica’yceo caaea/?
(5),(6).

, oaea, ui aeey ?ica’yceo u(x,t) caaea/? (5), (6) a??ia ioe?iea

.

A ae?oaiio ?icae?e? ?icaeyaea?oueny iae?i?eia ae?ioe/ia caaea/a Ae???oea
a iaeanoyo c oiieeie ii?iaeieiaie.

A i?ae?icae?e? 2.1 aeathoueny iinoaiiaea caaea/? oa iniiai? icia/aiiy.
Aeiaiaeyoueny ??ci? aeiiii?aei? oaa?aeaeaiiy oa oi?ioeth?oueny iniiaiee
?acoeueoao ?icae?eo.

oa caaeiaieueiythoue oiiae:

, j=1,…,n;

aeeiiai? ia??aiino?

.

ianooii? oiiae:

aeeiiothoueny aeeth/aiiy ,

aea

,

— a?aenoaiue a?ae oi/ee x aei iiiaeeie G;

b3) i?e aoaeue-yeiio s=1,2,… ii?yaeie n?iae iiiaeei

,

; iathoue i?noea aeeth/aiiy i?e i=1,…,I(s), l=1,…,L(i,s).

I?e oeueiio ii?yaeeii ne?i/aii? n?i’? iiiaeei aoaeaii iaceaaoe
iaea?eueoa oe?ea /enei p, aeey yeiai ? p+1 iiiaeei aeaii? n?i’? c?
ni?eueiith oi/eith.

:

oae?, ui

a?aeiia?aeii;

oaea, ui aeeiiai? ia??aiino?

,

,

— yeia??aa iao?eoey a?aeia?aaeaiiy u(x) a oi/oe? x.

I?eionoeii, ui i?e aoaeue-yeiio s

,

oa ?icaeyiaii iine?aeiai?noue e?aeiaeo caaea/

(7)

(8)

.

.

caaea/? (7),(8) oa ioe?ieo

? caaeiaieueiy? ioe?ieo

}.

??aiinoyie

,

,

, i?e,

, i?e,

.

iiiaeeie

.

. A i?ae?icae?e? aeiaiaeeoueny, ui oea ?icaeooy iiaeeeai cae?enieoe
oaeei /eiii, uia aeey iiiaeei, aeeiioaaeenue ianooii? oaa?aeaeaiiy:

oaea, ui

iiia?ii ia ia?aoeiathoueny;

b) ia? i?noea aeeth/aiiy

.

ye ?ica’ycie caaea/?

(9)

. Iaeiicia/ia ?ica’yci?noue caaea/? (9) aeoiaeeoue ?c caaaeueii? oai???
iiiioiiieo iia?aoi??a.

, k=1, …, K(i,s)

.

I?eionea?ii aeeiiaiiy ianooiii? oiiae:

aeeiiaia ??ai?noue

(10)

.

Iniiaiei ?acoeueoaoii ?icae?eo 2 ? ianooiia oai?aia.

? ocaaaeueiaiei ?ica’yceii caaea/?

(11)

(12)

Aeiaaaeaiith oe??? oai?aie i?enay/ai? i?ae?icae?ee 2.2, 2.3.

.

ia iniia? aneiioioe/iiai ?iceeaaeo.

A o?aoueiio ?icae?e? ?icaeyaea?ii iae?i?eio ia?aaie?/io caaea/o a
iaeanoyo c oiieeie ii?iaeieiaie.

A i?ae?icae?e? 3.1 aea?ii iinoaiiaeo caaea/? oa iniiai? icia/aiiy,
aeiaiaeeii ??ci? aeiiii?aei? oaa?aeaeaiiy oa oi?ioeth?ii iniiaiee
?acoeueoao ?icae?eo 3.

oa caaeiaieueiythoue oiiae:

, j=0,…,n ;

oae?, ui i?e an?o cia/aiiyo x, t, u, p aeeiiai? ia??aiino?

,

,

.

— ia?aoai?aiiy Oo?’? g(x,t) ii ci?ii?e t.

c? ne?i/aiith ii?iith

.

I?eionea?ii, ui aeeiiaia oiiaa:

oa caaeiaieueiy? ia??ai?noue

c aeayeith noaeith N.

ianooii? oiiae

,

oa oiiae b2), b3), l1), l2), c i. 2.1.

oa ?icaeyiaii iine?aeiai?noue eaac?e?i?eieo ia?aaie?/ieo caaea/

, (13)

, (14)

(15)

.

iiaeeeaa cai?ia oiiae (15) ia ianooiio

. (16)

, ii?ia a yeiio aea?oueny ??ai?noth

.

a??ia ?ioaa?aeueia oioiaei?noue

.

.

, e=0,…,M(i,s), ye? caaeiaieueiythoue oiiae:

i?noyoueny a?aeiia?aeii a ?ioa?aaeao

,

cia/aiiy ?o iaeaaeaoue a?ae??ceo [0,1];

aeeiio?oueny oioiaei?noue

;

a??i? ia??aiino?

.

ye ?ica’ycie ianooiii? caaea/?:

,

,

,

aecia/ai? a i?ae?icae?e? 2.1.

I?eionea?ii aeeiiaiiy ianooiii? oiiae:

aeeiiaia ??ai?noue

, (17)

.

Iniiaiei ?acoeueoaoii ?icae?eo ? ianooiia oai?aia.

? ?ica’yceii caaea/?

, (18)

, (19)

(20)

Aeiaaaeaiith oe??? oai?aie i?enay/ai? i?ae?icae?ee 3.2, 3.3.

, aea/aia aneiioioe/ia iiaaae?iea oe??? iine?aeiaiino?.

.

AENIIAEE

O aeena?oaoe?ei?e ?iaio? aia?oa aeine?aeaeaia ieoaiiy ona?aaeiaiiy
iae?i?eieo ae?ioe/ieo ? ia?aaie?/ieo e?aeiaeo caaea/ a iaeanoyo c
oiieeie ii?iaeieiaie oa io?eiai? ianooii? iniiai? ?acoeueoaoe:

1. Aeiaaaeai? ?ioaa?aeuei? oa iioi/eia? ioe?iee niaoe?aeueieo
iiaeaeueieo iae?i?eieo ae?ioe/ieo ? ia?aaie?/ieo e?aeiaeo caaea/.

2. Aea/aia aneiioioe/ia iiaaae?iea iine?aeiaiino? ?ica’yce?a caaea/
Ae???oea aeey iae?i?eieo ae?ioe/ieo ??aiyiue ae?oaiai ii?yaeeo a
iaeanoyo c oiieeie ii?iaeieiaie, iiaoaeiaaiee ei?aeoi? aeey iaaeeaeaiiy
oaei? iine?aeiaiino? ?ica’yce?a.

c p

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