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

?INOEOOO I?EEEAAeII? IAOAIAOEEE ? IAOAI?EE

UAEEIA Aiae??e Aai?a?eiae/

OAeE 517.9

Aaiethoe?y a?eueieo iiaa?oiae,

ca’ycaieo c ?ica’yceaie eaac?e?i?eieo ia?aaie?/ieo ??aiyiue
aeia?eueiiai ii?yaeeo,

ui ae?iaeaeothoueny.

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?oaoe??th ? ?oeiien.

?aaioa aeeiiaia a ?inoeooo? i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI
Oe?a?ie, i.Aeiiaoeuee.

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Oeoeia Aiae??e ?aaaiiae/ ,

?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie,

i?ia?aeiee iaoeiaee ni?a?ia?oiee.

Io?oe?eie iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

Oaae??a Aiaoie?e Oaaei?iae/,

?inoeooo i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie,

noa?oee iaoeiaee ni?a?ia?oiee,

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

Ai?iae?i Ieoaeei Ieaen?eiae/,

Aeiiaoeueeee aea?aeaaiee oi?aa?neoao, aeioeaio.

I?ia?aeia onoaiiaa Oa?uee?anueeee aea?aeaaiee oi?aa?neoao, eaoaae?a
iaoaiaoe/ii? o?ceee oa ia/enethaaeueii? iaoaiaoeee, i. Oa?uee?a.

Caoeno a?aeaoaeaoueny “ 22 ” ______aeiaoiy___ 1999 ?ieo i _17__
aiaeei? ia can?aeaii? niaoe?ae?ciaaiii? a/aii? ?aaee Ae 11.193.01 a
?inoeooo? i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie ca aae?anith:

340114, i.Aeiiaoeuee, aoe. ?. Ethenaiao?a, 74, aoaeeoi??y 309.

C aeena?oaoe??th iiaeia iciaeiieoeny a iaoeia?e a?ae?ioaoe? ?inoeoooo
i?eeeaaeii? iaoaiaoeee ? iaoai?ee IAI Oe?a?ie (340114, i.Aeiiaoeuee,
aoe. ?. Ethenaiao?a, 74).

Aaoi?aoa?ao ?ic?neaiee “ _18__ ” ____aa?aniy___________ 1999 ?ieo.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Eiaaeaanueeee I.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

AEOOAEUeIINOUe OAIE. ?iaioa i?enay/aia aea/aiith ieoaiiue, ca’ycaieo c
aeine?aeaeaiiyi iiaaae?iee ocaaaeueiaieo ?ica’yce?a caaea/? Eio? oa
a?aie/ieo caaea/ aeey eaac?e?i?eieo ia?aaie?/ieo ??aiyiiue n iiaea?eiei
ae?iaeaeaiiyi, ye ae?oaiai, oae ? a?eueo aenieeo ii?yaee?a, ui
aecia/a?oueny aaaeeea?noth oaeeo ??aiyiue i?e iieno ??ciiiai?oieo
o?ce/ieo yaeu. Ii/aoie o oeueiio iai?yieo aoei iieeaaeaii ?iaioaie
A.?.Aa?aiaeaooa, aea oia?oa iinoaaeaii ieoaiiy i?i aea/aiiy iiaaae?iee
iaae? iin?y ocaaaeueiaiiai ?ica’yceo ??aiyiiy iae?i?eiie o?eueo?aoe??
(aai oaieii?ia?aeiino?). Aeey oaeiai ??aiyiiy i?e aeayeeo
ni?aa?aeiioaiiyo ia ia?aiao?e o?eueo?aoe?? aoei aeyaeaii eean
?ica’yce?a, iin?e yeeo ?iciianthaeaeo?ony c? ne?i/aiiith oaeaee?noth.
sseui ??aiyiiy aieiae?? oaeei ?ica’yceii, oi eaaeooue, ui ia? i?noi
e?ioeaaa oaeaee?noue ?iciianthaeaeaiiy cao?thaaiue (EO?C).
Aeine?aeaeaiiyi EO?C i?enay/ai? ?iaioe oaeeo aaoi??a, ye I.A.Ie?eiee,
A.N.Eaeaoi?eia, *aeio-THe-E?iue, ?.Ea?oia?, N.I.Aioiioeaa, N.E.Oia?aa,
J.I.Diaz, L.Veron oa ?io? aeey ??aiyiue ae?oaiai ii?yaeeo, A.?.Oeoeia,
F.Bernis aeey ??aiyiue aenieiai ii?yaeeo. sse aeyaeeinue, oaeaee?noue
?inoo oaiia?aoo?e (a oa?i?iao ??aiyiiy oaieii?ia?aeiino?) o aoaeue-ye?e
oi/oe? na?aaeiaeua caeaaeeoue a?ae i?inoi?iaiai i?io?eth a ieie? oe???
oi/ee. sseui i?io?eue a aeinoaoi?e i??? “oa?aiooee”, oi oaiia?aoo?a
iiaea ia ci?ithaaoeny aai neaaei ci?ithaaoeny ca aeayeee /an a iaaeao
ei?aeiio. sseui ??aiyiiy aieiae?? oaeei ?ica’yceii, oi eaaeooue, ui ia?
i?noi aoaeo ?ia?oe?? (ne?i/aiii? aai iane?i/aiii?). Oaeei /eiii, oaeo
iayaiino? ?ia?oe?? caeaaeeoue a?ae iiaaae?iee ii/aoeiai? ooieoe?? a
iaio?e iaae? ei?aeiio iin?y. Oia?oa aeine?aeaeaiiy aoaeoo ?ia?oe??
i?iaiaeeeinue o ?iaio? A.A.Naia?nueeiai, ?.I.Niaiey, iio?i o ?iaioao
A.N.Eaeaoi?eiaa, ?.Ea?oia?a, L.A.Peletier. Aeey ??aiyiiy oeio
“iia?eueii?” aeeooc?? i?e iayaiino? iiaeeiaiiy aoaeo ?ia?oe?? aea/aany a
?iaioao oaeeo aaoi??a, ye A.N.Eaeaoi?eia, ?.Ea?oia?, TH.A.?eeia,
N.I.Aioiioeaa, A.Friedman, M.A.Herrero, J.I.Diaz, L.Veron oa ?io?. A
oeeo ?iaioao, a oaeiae o ?iaioao ?ioeo aaoi??a io?eiai? ioe?iee /ano
cao?eiee.

I?e aeineoue neeueiiio iiaeeiaii? iiaea noaoeny oae, ui iaa?oue ca
iane?i/aiiee i?ii?aeie /ano oaiei i?iieeia eeoa ia e?ioeaao a?aenoaiue
(aoaeo eieae?caoe??). A?eueo oiai, aiii iiaea i?eaanoe aei cai?ioiueiai
?ooo o?iioo (C?O), oa iaa?oue aei iiaiiai cieeiaiiy ?ica’yceo (aai
noaa?e?caoe?? o oa?i?iieia?? Eaeaoi?eiaa). Eieae?caoe?y a caaea/? Eio?
aoea anoaiiaeaia a ?iaioao E.E.Ia?o?iniia, E.A.Iaaeiaa, iio?i
A.N.Eaeaoi?eiaa, B.F.Knerr, oa ?ioeo, aea oaeiae io?eiai? e?eoa??? ??
?nioaaiiy. C?O aea/aany, iai?eeeaae, ?.Ea?oia?ii aeey ??aiyiue ae?oaiai
ii?yaeeo, A.?.Oeoeiaei aeey ??aiyiue aenieiai ii?yaeeo. Aoaeo
noaa?e?caoe?? aea/aany o ?iaioao A.N.Eaeaoi?eiaa, M.A.Herrero,
A.Friedman, J.L.Vazquez oa ?ioeo. E??i oiai, aoei aeyaeaii, ui a oe?e
neooaoe??

iiaeeeaa a?eueo oneeaaeiaia aaiethoe?y iin?y, a naia, i?e aeayeeo
iaiaaeaiiyo ia iiaaae?ieo ii/aoeiai? ooieoe?? oa ia ia?aiao?e ??aiyiiy
iin?e ?ica’yceo nii/aoeo aoaea ?icoe?thaaoeny, a iio?i caoaeoaaoeny aae
aei iiaiiai cieeiaiiy (o aeiaaeeo, yeui iin?e ii/aoeiai? ooieoe?? aoa
eiiiaeoiei). Oae?e ?ica’ycie a iaeiii??iiio aeiaaeeo io?eiaii
?.Ea?oia?ii, eiai aaaaoii??ia aiaeia?y ciaeaeaia E.E.Ia?o?iniiii.
Caoaaaeeii, ui aeine?aeaeaiiy i?iaiaeeeinue eeoa aeey ??aiyiue ae?oaiai
ii?yaeeo, yeui ?ioa ia iaiai?aii iniaenoi.

Aeey ??aiyiiy oeio “oaeaeei?” aeeooc?? c iiaeeiaiiyi aenieiai ii?yaeeo
oaeoe iayaiino? ?ia?oe?? oa C?O aoee aeyaeaie A.?.Oeoeiaei i?e
“?ioaineaiiio” iiaeeiaii? oa aeinoaoiuei oa?aiooiio i?io?e? aeayei?
?ioaa?aeueii? ii?ie ii/aoeiai? ooieoe?? a iaaeao ei?aeiio. Aeooaeueiei ?
iien noa?oiai? iiaaae?iee ocaaaeueiaiiai ?ica’yceo eaac?e?i?eiiai
ia?aaie?/iiai ??aiyiiy aeia?eueiiai ii?yaeeo a caeaaeiino? a?ae
eieaeueieo aeanoeainoae ii/aoeiai? ooieoe?? oa ia?aiao??a ??aiyiiy. ?yae
?acoeueoao?a o oeueiio iai?yieo io?eiaii o ia?oiio ?icae?e?.

Inoaii?i /anii aeoeaiiio aea/aiith i?aeeyaathoue i?oai? caaea/? aeey
??cieo eean?a ia?aaie?/ieo ??aiyiue ae?oaiai ii?yaeeo o i?eiouaii?, ui
?ica’ycie “ci?ith?oueny” ia iaae? o oae caaiiio a?aie/iiio ?aaeei? c
caaino?aiiyi, oiaoi a?aie/ia ooieoe?y iane?i/aiii c?inoa? o aeayeiio
?icoi?ii?, yeui /an t i?yio? aei /ano caaino?aiiy T. Ni?aa?aeiioaiiy
i?ae oaiiaie i?aeaiaeo aia?a?? oa aeanoeainoyie na?aaeiaeua aecia/athoue
iiaaae?ieo ?ica’yceo. sse aeyaeeiny, oaeaee?noue iinooio aia?a?? c
a?aieoe? iiaea aooe oae iiaiaeaeaia c aioo??oieie aeanoeainoyie
na?aaeiaeua, ui oaiei aoaea ?iciianthaeaeeaaoenue ??aiii??ii ii anueiio
i?io?eth. I?e a?eueo iia?eueiiio i?aeaaaeaii? aia?a?? oaiei
cina?aaeaeo?ony iiaeeco ei?aeiio, oa iiaea aooe eieae?ciaaiei o aeayei?
eoe? e?ioeaaiai ?aae?ono.

Ciaoiaeaeaiiy oiia eieae?caoe?? oa iien no?oeoo?e iiiaeeie
iane?i/aiiino? ?ica’yceo ? iniiaieie ieoaiiyie a iaaeao oe??? oaiaoeee.
Ia?a?nii oaea aea/aiiy i?iaiaeeeinue ia i?eeeaaeao caaea/? Eio?-Ae???oea
aeey iaeiii??iiai iiaeaeueiiai ??aiyiiy iae?i?eii? oaieii?ia?aeiino?
(A.A.Naia?nueeee, A.A.Aaeaeo?iiia, N.I.Eo?aethiia, A.I.Ieoaeeia), aeey
yeiai io?eiaii e?eoa??e eieae?caoe?? i?e “aei?noeeo” oiiaao ia a?aie/io
ooieoe?th. Ineaaeaiiy oeeo oiia aoei cae?eniaii a ?iaio? B.H.Gilding,
M.A.Herrero. Ocaaaeueiaiiy io?eiaieo ?acoeueoao?a aeey caaea/?
Eio?-Iaeiaia aoei i?iaaaeaii a ?iaio? C.Cortazar, M.Elgueta, a ye?e
oaeiae io?eiai? e?eoa??? eieae?caoe?? oa iaiaaeaiiino? ?ica’yceo o
aoaeue-ye?e no?iai aioo??oi?e i?aeiaeano?. A ?iaio? B.H.Gilding,
J.Goncerzewicz io?eiaiee a?eueo neeueiee e?eoa??e iaiaaeaiino? ?ica’yceo
caaea/? Eio?-Iaeiaia, oa oaeiae c?iaeaie ocaaaeueiaiiy ia aaaaoiaei??iee
aeiaaeie. Aeine?aeaeaiiyi a?aie/ieo ?aaeei?a c caaino?aiiyi a caaea/?
Eio?-Ae???oe? aeey ??aiyiiy iae?i?eiie oaieii?ia?aeiino? c iiaeeiaiiyi
oa aeayeiai eiai ocaaaeueiaiiy i?iaiaeeeinue o ?iaioao O.A.Aaaeoea?aa.

A ca’yceo c oeei aeooaeueiei ? iiaeaeueoa aea/aiiy a?eueo caaaeueieo
ia?aaie?/ieo ??aiyiue c iaio ?aaoey?ieie oiiaaie ia a?aie/io ooieoe?th
oa iien iiaaae?iee ?ica’yceo caaea/? Eio?-Iaeiaia. A ae?oaiio oa
o?aoueiio ?icae?eao o oeueiio iai?yieo io?eiaii ?yae ?acoeueoao?a. A
/aoaa?oiio ?icae?e? oaea aeine?aeaeaiiy i?iaiaeeeinue aeey aeayeiai
ocaaaeueiaiiy eeane/iiai ??aiyiiy oaieii?ia?aeiino? i?e a?aenooiino?
iiaeeiaiiy, oaeiae i?e ineaaeaii? oiia ia aeaaee?noue a?aie/ii?
ooieoe??.

IAOEIAA IIA?CIA. Aeena?oaoe?y i?enay/aia aeine?aeaeaiith aeanoeainoae
caaaeueieo ia?aaie?/ieo ??aiyiue, oa?aeoa?iith iniaeea?noth yeeo ?
iiaea?eia ae?iaeaeaiiy. Iniiai? ?acoeueoaoe ?iaioe iieyaathoue o
ianooiiiio:

1) iaea?aeaii oi/ii oiiae iayaiinoi aeanoeainoae iia?oeiy oa ciaioaiiy
?icii?ia iiniy; 2) io?eiaii ioeiiee, yei iiaiinoth iienothoue noa?oiaee
?oo iiniy ?ica’yceo a caeaaeiinoi aiae eieaeueieo aeanoeainoae
ii/aoeiai? ooieoei?; 3) io?eiaii oiiae, yei aa?aioothoue iayaiinoue
eieaeicaoei? oa iaiaaeaiinoi ?ica’yce?a caaea/? Eioe-Iaeiaia aeey
ia?aaiei/ieo ?iaiyiue caaaeueiiai aeaeyaeo, o aeiaaeeo, eiee a?aie/ia
ooieoeiy iaiaiaaeaii c?inoa? ?c c?inoaiiyi /ano aei aeayeiai o?eniaaiiai
O; 4) ciaioaii oiiae ia ?aaoey?iinoue a?aie/ii? ooieoei?, yei oaeiae
aa?aioothoue aoaeoe , ia?a?aoiaaii o ioieoo 3); 5) ocaaaeueiaii
?acoeueoaoe i?i iaiaaeai?noue ?ica’yceo caaea/i Eioi-Iaeiaia aeey
??aiyiiy, yea aeeth/a? aei naaa eeane/ia ?iaiyiiy oaieii?iaiaeiinoi,
iaeaea ne??cue a aoaeue-yei? no?iai aioo?ioiuei? i?aeiaeanoi o aeiaaeeo
a?aie/iiai ?aaeeio c caaino?aiiyi.

An? ?acoeueoaoe iaea?aeaii aaoi?ii iniaenoi. Aiie ? iiaeie ? no?iai
iaa?oioiaaieie. Iniiai? ?acoeueoaoe ?iaioe aieeaathoue ia iiaeaeueoee
?icaeoie aeine?aeaeaiue aeanoeainoae ?ica’yce?a ??cieo ia?aaie?/ieo
caaea/.

OAI?AOE*IA OA I?AEOE*IA CIA*AIIss. ?acoeueoaoe aeena?oaoe?? iathoue
oai?aoe/iee oa?aeoa?. Aiie iiaeooue aooe aeei?enoai? aeey
ii??aiyeueiiai aiae?co ??cieo aeanoeainoae ?ica’yce?a caaaeueieo
ia?aaie?/ieo caaea/, ui ae?iaeaeothoueny.

CA’ssCIE C IEAIAIE IAOEIAI-AeINE?AeIEO ?IA?O ?INOEOOOO. Aeine?aeaeaiiy
ii aeena?oaoe?? i?iaiaeeeenue o 1993-1998 ?ieao ? aoee ia?aaeaa/ai?
ieaiaie iaoeiaeo aeine?aeaeaiue a?aeae?e?a iae?i?eiiai aiae?co oa
??aiyiue o /anoeiieo iio?aeieo ?inoeoooo i?eeeaaeii? iaoaiaoeee oa
iaoaieee IAI Oe?a?ie.

IOAE?EAOe??. Ca oaiith aeena?oaoe?? iioae?eiaaii 5 ae?oeiaaieo i?aoeue,
a oiio /ene? 4 a noaooyo iaoeiaeo aeo?iae?a oa 1 o iaoa??aeao
i?aeia?iaeii? eiioa?aioe??.

INIAENOEE AIANIE CAeIAOAA*A. A ?iaioao, ui iaae?oeiaai? o ni?aaaoi?noa?
caeiaoaa/o iaeaaeaoue oae? ?acoeueoaoe. A ?iaio? [2] — aeieac oai?ai
1,3,4,5 ca aeeeth/aiiyi eaii 3.1, 3.2. A ?iaio? [3] — aeieac ioieo?a 3)
a oa?aiao 1-4. A ?iaio? [5] — aeieac oai?aie 2.

AI?IAAOe?ss ?ACOEUeOAO?A AeENA?OAOe??. Iniiai? ?acoeueoaoe aeena?oaoe??
aeiiia?aeaeeny ia:

— I?aeia?iaei?e eiio. “ Nonlinear Partial Differential equations”,
Ke?a, na?iaiue 1997,

— aocianueeee eiioa?aioe?? AeiiAeO ” Iaoaiaoeea, oeceea, yeieiaey.”
Aeiiaoeuee, o?aaaiue 1997,

— nai?ia?ao a?aeae?e?a iae?i?eiiai aiae?co oa ??aiyiue o /anoeiieo
iio?aeieo ?III IAI Oe?a?ie (Aeiiaoeuee, ea?. aeaaeai?e. IAI Oe?a?ie
?.A.Ne?eiiee).

NO?OEOO?A OA IANssA AeENA?OAOe??. ?iaioa aeeeaaeaia ia 137 noi??ioeyo oa
neeaaea?oueny c? anooio, /ioe?ueio ?icae?e?a oa nieneo e?oa?aoo?e ?c 59
iaeiaioaaiiue.

INIIAIIE CIINO.

O anooii iaa?oioiao?oueny aeooaeueiinoue oaie aeena?oaoeieii? ?iaioe,
iaoa oa caaea/i aeineiaeaeaiiy, iaeyae ?iaio, iia’ycaieo c oei?th
oaiaoeeith, ie?aneththoueny iniiaii aoaie ?icaeoeo iaoeiai? aeoiee o
aeaiiie aaeoci.

A ia?oiio ?icaeiei aeineiaeaeo?oueny noa?oiaee ?oo iaaei iiniy
?ica’yceo ianooiiii caaea/i Eioi:
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u(0,x)
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(2)

aea
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oiiae eia?oeeoeaiinoi i c?inoaiiy

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0000 (3)

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0500 (4)

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(5)

N(m) iicia/aa eieueeinoue ?icieo n-ii?ieo ioeueoiiiaeaenia aeiaaeeie ia
aieueo iiae m.

A ia?aa?aoi 1.1 iiaeaaoueny iinoaiiaa caaea/i.

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iaaei

iiniy ocaaaeueiaiiai ?icayceo caaea/i (1), (2) a caeaaeiinoi aiae
niiaaiaeiioaiue

ia ia?aiao?e ?iaiyiiy oa aiae iiaaaeiiee ooieoeii:

f(s)=picscalex264010009000003d301000002001700000000000500000009020000000
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00300000000000000

Iai?eeeaae, noi?ioeueiaaia ianooiia

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00,

aea

S =c_1[
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02022253797374656d00cc040000002d01000004000000f00101000300000000000000)]
, 00,

aea

S =0

3) eiee

f(s)
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57720526f6d616e2043797200cc67040000002d01000008000000320a40063c060100000
0300008000000320a4006f10001000000f00008000000320a00046e02010000002900080
00000320a00043c0101000000280008000000320ac0016e0201000000290008000000320
ac0013c0101000000280017000000fb0240ff0000000000009001000000cc04020010546
96d6573204e657720526f6d616e2043797200cc67040000002d01010004000000f001000
008000000320a5001500401000000310010000000fb0280fe00000000000090010000000
20002001053796d626f6c0002040000002d01000004000000f001010008000000320a400
66c0401000000ae0008000000320a0004180501000000a50008000000320a00044803010
00000ae0017000000fb0280fe0000000000009001010000cc0402001054696d6573204e6
57720526f6d616e2043797200cc67040000002d01010004000000f001000008000000320
a4006740301000000730008000000320a40060202010000008f0008000000320a4006280
001000000950008000000320a0004cc0101000000730008000000320a000440000100000
0770008000000320ac001fe0201000000730008000000320ac001cc01010000007300080
00000320ac001400001000000770010000000fb0200ff000000000000900101000002000
2001053796d626f6c0002040000002d01000004000000f001010008000000320a1001ac0
30100000061000a00000026060f000a00ffffffff01000000000010000000fb021000070
000000000bc02000000cc0102022253797374656d00cc040000002d01010004000000f00
1000003000000000000ffoiaei

aea

s=s( t)

sse ianeiaeie io?eiaii oaei ?acoeueoaoe:

A) sseui
u_0(x)picscalex1000100090000035c0100000200170000000000050000000902000000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, oiaei

n aeayeie
l_00,

aea

S =c_1[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(C_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)]
, 00,

aea

S =0

Oaeei /eiii iiaiinoth iienaiee noa?oiaee ?oo iaaei iiniy ocaaaeueiaiiai
?ica’yceo caaea/i (1), (2).

A ae?oaiio ?icaeiei ?icaeyaeathoueny oae caaii a?aie/ii ?aaeeie c
caaino?aiiyi.

I?e aeineiaeaeaiii oaeeo ?aaeeiia iniiaieie ieoaiiyie a ciaoiaeaeaiiy
oi/ieo oiia eieaeicaoeii ?ica’yceo oa iien no?oeoo?e eiai iiiaeeie
iaiaiaaeaiinoi.

A ia?aa?aoi 2.1 ie?aneththoueny iniiaii aoaie ?icaeoeo iaoeiaii aeoiee o
oei i aaeoci.

A ia?aa?aoi 2.2 ?icaeyaeoaoueny ii/aoeiai-e?aeiaa caaea/a a iaeanoi
Q=(0,T)picscalex10001000900000388000000020012000000000005000000090200000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aea

A?aie/ia ooieoeiy f a neiaeii ia aeayeii f(t,x) oaeii, ui

Iiaaaeiieo a?aie/iiai ?aaeeio aoaeaii oa?aeoa?ecoaaoe ooieoeiath

Iaoae

Oai?aia 3. Iaoae aeeiiaii oni ia?a?aoiaaii oiiae ia caaeaii ooieoeii
caaea/i.

Iaoae

0R_0, oa

oi

Oai?aia 4. Iaoae aeeiiaii oiiae Oai?aie 3.

Oiaei

aeey aoaeue-yeii no?iai aioo?ioiueii iiaeiaeanoi.

A ia?aa?aoi 2.3 aeiaaaeaii oei oai?aie.

Oaeei /eiii, ciaeaeaii oiiae, yei aa?aioothoue eieaeicaoeith oa
iaiaaeaiinoue

?ica’yceo. Oi/iinoue oeeo oiia iiaeoaa?aeaeoaony ?acoeueoaoaie
A.A.Naia?nueeiai,

A.A.Aaeaeoiiiiaa, B.H.Gilding, M.A.Herrero.

A o?aoueiio ?icaeiei ?icaeyaeathoueny a?aie/ii ?aaeeie c caaino?aiiyi o
aeiaaeeo

iayaiinoi aani?aoeii.

A ia?aa?aoi 3.1 ?icaeyaeaaoueny iaa/aeueii-e?aeiaa caaea/a a iaeanoe

Ooieoeiy, aiaeiiaiaeia ca iiaeeiaiiy, caaeiaieueiya

O.A.Aaaeoeaaaei aeey iaio caaaeueiiai ?iaiyiiy aoei aeiaaaeaii, ui oiiaa

aeinoaoiy aeey eieaeicaoeii oa iaiaaeaiinoi ?ica’yceo i?e aoaeue-yeiio
c?inoaiii

a?aie/iii ooieoeii, aea i?e aeinoaoiuei «aei?noeeo» oiiaao ia ii
?aaoey?iinoue.

A ia?aa?aoi 3.2 noi?ioeueiaaiee aiaeiai/iee ?acoeueoao aeey aieueo
caaaeueiiai ?iaiyiiy c iaio ?aaoey?ieie oiiaaie ia a?aie/io ooieoeith.

Oai?aia 5 Iaoae aeeiiaii oni ia?a?aoiaaii oiiae ia caaeaii ooieoeii
caaea/i.

Iaoaeoiaei inioa R_0=R_0( n, p, q, d,|| u_0||, 1R_0, oi i?e aoaeue-yeiio c?inoaiii
a?aie/iii ooieoeii (oiaoi i?e aoaeue-yeiio c?inoaiii ooieoeii F(t))

Oai?aia 6. Iaoae aeeiiaii oiiae oai?aie 5. Oiaei

aeey aoaeue-yeii no?iai aioo?ioiii iiaeiaeanoi G.

A ia?aa?aoi 3.3 aeiaaaeaii oei ?acoeueoaoe.

Oaeei /eiii o o?aoueiio ?icaeiei aeiaaaeaii, ui i?e aoaeue-yeiio
c?inoaiii a?aie/iii ooieoeii (oiaoi i?e aoaeue-yeiio c?inoaiii ooieoeii
F(t)) ?ica’ycie aoaea eieaeiciaaiee o eoei neii/aiiiai ?aaeiona oa
iaiaaeaiee o oeueiio eoei.

Aaaeeeaith /anoeiith aeineiaeaeaiue, ui i?iaiaeeeeny o ae?oaiio oa
o?aoueiio ?icaeieao, a iaiaaaiiy io?eiaoe aiaeiai/ii ?acoeueoaoe o
e?eoe/iiio aeiaaeeo

$p=q$ a caaea/ao c caaino?aiiyi. A /aoaa?oiio ?icaeiei iaea?aeaii
?acoeueoaoe i?i iaiaaeaiinoue ocaaaeueiaiiai ?ica’yceo o oeueiio
aeiaaeeo.

Oai?aia 7.Iaoae

0R_0, oi, yeui

aea

oi

Oaeei /eiii, o /aoaa?oiio ?icaeiei io?eiaii e?eoe/iee ?aaeei c
caaino?aiiyi,

i?e yeiio ?icaycie ?iaiyiiy, yea aeeth/aa aei naaa eeane/ia ?iaiyiiy
oaieii?iaiaeiinoi,

aoaea iaiaaeaiei a aoaeue-yeii no?iai aioo?ioiueii iiaeiaeanoi
ii/aoeiaii iaeanoi.

AENIIAEE.

Iaea?aeaii oi/ii oiiae iayaiinoi aeanoeainoae iia?oei? oa ciaioaiiy
?icii?ia iiniy.

Io?eiaii ioeiiee, yei iiaiinoth iienothoue noa?oiaee ?oo iiniy ?ica’yceo
a caeaaeiinoi aiae eieaeueieo aeanoeainoae ii/aoeiai? ooieoei?.

Io?eiaii oiiae, yei aa?aioothoue iayaiinoue eieaeicaoei? oa
iaiaaeai?noue ?ica’yce?a caaea/ Eioe-Iaeiaia aeey ia?aaiei/ieo ?iaiyiue
caaaeueiiai aeaeyaeo, o aeiaaeeo, eiee a?aie/ia ooieoeiy iaiaiaaeaii
c?inoa? ?c c?inoaiiyi /ano aei aeayeiai o?eniaaiiai O.

Ciaioaii oiiae ia ?aaoey?iinoue a?aie/ii? ooieoei?, yei oaeiae
aa?aioothoue aoaeoe , ia?a?aoiaaii o ioieo? 3).

Ocaaaeueiaii ?acoeueoaoe i?i iaiaaeai?noue ?ica’yceo caaea/i
Eioi-Iaeiaia aeey ??aiyiiy, yea aeeth/a? aei naaa eeane/ia ?iaiyiiy
oaieii?iaiaeiinoi, iaeaea ne??cue a aoaeue-ye?e no?iai aioo?ioiuei?
i?aeiaeanoi o aeiaaeeo a?aie/iiai ?aaeeio c caaino?aiiyi.

Ani ?acoeueoaoe iaea?aeaii aaoi?ii iniaenoi. Aiie ? iiaeie i aeieeaaeii
iaa?oioiaaieie. Iniiaii ?acoeueoaoe ?iaioe aieeaathoue ia iiaeaeueoee
?icaeoie aeineiaeaeaiue aeanoeainoae ?ica’yce?a ?icieo ia?aaiei/ieo
caaea/.

NIENIE IIOAEIEIAAIEO I?AOeUe CA OAIITH AeENA?OAOeI?.

1. Shchelkov A. G. Regime with peaking for quasilinear parabolic
equations of higher order with absorption. Book of Abstracts of
International Conference «Nonlinear Partial Differential Equations»,
Kiev, August 1997.

2. Oeoeia A. A., Uaeeia A.A. Aeeiaieea iineoaeae yia?aaoe/aneeo ?aoaiee
niaoaiiuo caaea/ aeey eaaceeeiaeiuo ia?aaiee/aneeo o?aaiaiee
i?iecaieueiiai ii?yaeea. Ecaanoey ?AI, na?. Iao., N3. 1998 n.175-201.

3. Oeoeia A.A., Uaeeia A.A. Ia/aeueiay yaiethoeey iineoaeae ?aoaiee
caaea/e Eioe aeey eaaceeeiaeiuo ia?aaiee/aneeo o?aaiaiee i?iecaieueiiai
ii?yaeea. O?oaeu EIII IAI Oe?aeiu «Iiaeaee?iaaiea iai?a?uaiuo e
aeene?aoiuo nenoai» oii2, 1998, n.148-158.

4. Uaeeia A.A. Iaia?aie/aiiua a?aie/iua ?aaeeiu a caaea/ao aeey
eaaceeeiaeiuo ia?aaiee/aneeo o?aaiaiee n aani?aoeeae. O?oaeu EIII IAI
Oe?aeiu «Iiaeaee?iaaiea iai?a?uaiuo e aeene?aoiuo nenoai» oii2, 1998,
n.158-167.

5. Oeoeia A.E., Uaeeia A.A. A?aie/iua ?aaeeiu n iaino?aieai aeey iaueo
eaaceeeiaeiuo ia?aaiee/aneeo o?aaiaiee a iiiaiia?iuo iaeanoyo. Iao. na.
1999, ?3, no?. 129-160.

AIIOAOeIss

Uaeeia A.A. Aaiethoeiy aieueieo iiaa?oiae, ca’ycaieo c ?ica’yceaie
eaacieiiieieo ia?aaiei/ieo ?iaiyiue aeiaieueiiai ii?yaeeo, ui
ae?iaeaeothoueny.-?oeiien.

Aeena?oaoeiy ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
oiceei-iaoaiaoe/ieo iaoe ca niaoeiaeueiinoth 01. 01. 02 —
aeeoa?aioeiaeueii ?iaiyiiy.-Iinoeooo i?eeeaaeii? iaoaiaoeee i iaoai?ee
IAI Oe?a?ie, Aeiiaoeuee, 1999.

Aeena?oaoeiy i?enay/aia aeineiaeaeaiith aeanoeainoae caaaeueieo
ia?aaiei/ieo ?iaiyiue, oa?aeoa?iith iniaeeainoth yeeo ? iiaeaieia
ae?iaeaeaiiy. Iniiaii ?acoeueoaoe ?iaioe iieyaathoue o ianooiiiio:

Iaea?aeaii oi/ii oiiae iayaiinoi aeanoeainoae iia?oeiy oa ciaioaiiy
?icii?ia iiniy.

Io?eiaii ioeiiee, yei iiaiinoth iienothoue noa?oiaee ?oo iiniy ?ica’yceo
a caeaaeiinoi aiae eieaeueieo aeanoeainoae ii/aoeiai? ooieoei?.

Io?eiaii oiiae, yei aa?aioothoue iayaiinoue eieaeicaoei? oa
iaiaaeai?noue ?ica’yce?a caaea/ Eioe-Iaeiaia aeey ia?aaiei/ieo ?iaiyiue
caaaeueiiai aeaeo, o aeiaaeeo, eiee a?aie/ia ooieoeiy iaiaiaaeaii
c?inoa? c ?inoii /ano aei aeayeiai o?eniaaiiai O.

Ciaioaii oiiae ia ?aaoey?iinoue a?aie/ii? ooieoei?, yei oaeiae
aa?aioothoue aoaeoe , ia?a?aoiaaii o ioieo? 3).

Ocaaaeueiaii ?acoeueoaoe i?i iaiaaeai?noue ?ica’yceo caaea/i
Eioi-Iaeiaia aeey eeane/iiai ?iaiyiiy oaieii?iaiaeiinoi iaeaea anthaee a
aoaeue-ye?e no?iai aioi?ioii? i?aeiaeanoi o aeiaaeeo a?aie/iiai ?aaeeio
c caaino?aiiyi.

?acoeueoaoe aeena?oaoei? iathoue oai?aoe/iee oa?aeoa?. Aiie iiaeooue
aooe aeei?enoaii aeey ii?iaiyeueiiai aiaeico ?icieo aeanoeainoae
?icayce?a caaaeueieo ia?aaiei/ieo caaea/.

Eeth/iai neiaa: ia?aaiei/ii ?iaiyiiy, aeeoociy, aani?aoeiy, noa?oiaee
?oo, ?aaeeie c caaino?aiiyi, eieaeicaoeiy, iaiaaeaiinoue.

Uaeeia A.A. Yaiethoeey naiaiaeiuo iiaa?oiinoae, naycaiiuo n ?aoaieyie
eaaceeeiaeiuo au?iaeaeathueony ia?aaiee/aneeo o?aaiaiee i?iecaieueiiai
ii?yaeea. ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01. 01. 02 —
aeeooa?aioeeaeueiua o?aaiaiey. — Einoeooo i?eeeaaeiie iaoaiaoeee e
iaoaieee IAI Oe?aeiu, Aeiiaoee, 1999.

A aeenna?oaoeee eco/aaony aii?in i oii, eaeei ia?acii eieaeueiua
naienoaa iaeioi?ie eioaa?aeueiie ii?iu ia/aeueiie ooieoeee (i?e
?acee/iuo niioiioaieyo ia ia?aiao?u o?aaiaiey) aeeytho ia oa?aeoa?
aeaeaeaiey a?aieoeu iineoaey ?aoaiey au?iaeaeathuaainy ia?aaiee/aneiai
o?aaiaiey i?iecaieueiiai ii?yaeea i?e iaeuo cia/aieyo a?aiaie. Eae
ieacaeinue, i?e aeinoaoi/ii neeueiii iiaeiuaiee oaiea (a oa?ieiao
o?aaiaiey oaieii?iaiaeiinoe) aeey o?aaiaiey oeia “iaaeeaiiie” aeeooocee
nouanoaotho «e?eoe/aneea» ia?aie/aiey ia iiaaaeaiea yoie ii?iu, oaeea,
/oi iineoaeue eeai oiaiueoaaony, eeai inoaaony iaiiaeaeaeiui, eeai
ia/eiaao aeaeaaoueny a noi?iio naiaai oaaee/aiey. Aeaiu

ioeaiee noa?oiaie nei?inoe aeaeaeaiey a?aieoeu iineoaey. Eae neaaenoaea
iieo/ai oaeie ?acoeueoao: anee iineoaeue ia/aeueiie ooieoeee eiiiaeoai,
oi iineoaeue ?aoaiey nia/aea aoaeao ?anoe?youeny, a caoai ia/iao
noaeaoueny, oi anoue ?aoaiea aoaeao iaeaaeaoue naienoaii, aiaeiae/iui
naienoao ?aoaiey ?.Ea?oia?a. Yoi icia/aao, /oi ?aoaiea ia
?ani?ino?aieony aeaeaa iaeioi?iai oa?a eiia/iiai ?aaeeona (yooaeo
eieaeecaoeee) e aeaaea ia?aoeony a ioeue ca eiia/iue i?iiaaeooie
a?aiaie. I?e ae?oaeo cia/aieyo ia ia?aiao?u o?aaiaiey, iaeiaei oaeaea
i?e q

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