On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables

A mixed problem with nonlocal conditions on a space variable is considered for a system of quasilinear first-order hyperbolic equations with two independent variables. The sufficient conditions of solvability of this system are given.

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Бібліографічні деталі
Дата:1993
Автори: Kmit, I. Ya., Кміть, І. Я.
Формат: Стаття
Мова:Українська
Англійська
Опубліковано: Institute of Mathematics, NAS of Ukraine 1993
Онлайн доступ:https://umj.imath.kiev.ua/index.php/umj/article/view/5934
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
_version_ 1860512160222806016
author Kmit, I. Ya.
Кміть, І. Я.
author_facet Kmit, I. Ya.
Кміть, І. Я.
author_sort Kmit, I. Ya.
baseUrl_str https://umj.imath.kiev.ua/index.php/umj/oai
collection OJS
datestamp_date 2020-03-19T09:21:13Z
description A mixed problem with nonlocal conditions on a space variable is considered for a system of quasilinear first-order hyperbolic equations with two independent variables. The sufficient conditions of solvability of this system are given.
first_indexed 2026-03-24T03:24:22Z
format Article
fulltext Y)lK5 17.95 I. 51. KMiT1,, acn. (JlbBiR. y11-T) IlPO O)lHY HEJ19KAJibHY 3A)lA qy )lJIH KBA3IJIIHIU: HOI r1nEP6OJIIqHOI CHCTEMU IlEPllIOro IlOPH,[(KY 3 )lBOMA HE3AJIE)KHHMU 3MIHHHMU A mixed problem wit h nonlocal conditi o ns in a space variable is considered for the systems of quasi­ linear fi rst-order hyperbolic equati o ns wi th two independent variables. The sufficient conditions for the solvability of the system are g ive n. )lJIJI CHCTeMH KBa3iJ1i11 iA HHX r i11cp60JJi'I HHX piBIIRH b ncpwor·o nopRAKY 3 ABOMa HC 3aJJC)KfiHMH 3MiH­ HHMH po3rJlj([laE:TbCj( MiWa Ha 3a[la<1a, 3 IICJIOKaJJbHHM H YMOBaMH 110 npoc-roponiA 3Mi1rniA. Hano­ t\j(TbCj( nocTaTlli YMOBH po3B ';i3yoa11oc-r i. rinep6oni'-III i CHCTeMH 3 t(l30Ma IIe3aJie)KIIHMH 3MiHIIHMH AOCJiiJ..l)KYBaJIHCb 6araTbMa anropaMH. Po3r JI½J..la.i lHCb ½K Knacwmi 3aAa'li, TaK i 3a,[J.a'-!i 3 uep03AiJieHHMH a6o iuTerpaJibllHMH YMOBaMH. TaK, neKJiaCH'IHi 3a,[J.a'li AOCJiiA)KYBaJIHCb y po6orax [ I - 81 . E Jm3bKi 3atJ.a'li po3rm1AaJIHCb y po6ornx [9 - 11]. Hexart Ys - KpH13i, 3aJJ.aHi piBII½HH½MH x = a,(t), s = 0, m +I, npH'-IOMY a 5 E C 1l0, 71, as+ 1(t)>a 5(t) np1-1 t E (0, T] . B o6nacri QT= {(x, f): a 0(t) < x< < am+l(t) , 0 < f < T) po3rmm eMO CHCTeMy u;1 - A, (x, t , u)u ix = J; (x, t, u), = Gi. (1) EyJJ.eMo np1mycKaT1-1, mo nc i ¢y11Kui1 A; (x, t , u), J; (x, t, u) BH3Ha'leHi n o6nacTi Dlt = Q 1x { u: u E 1R 11 , II II II= m~I It , I 5 Mo}, BHMipHi Ta o6Me)KeHi no MOAYJIIO B 0 i = I, 11 DL0 KOHCTHHTaMH A i F BiJJ.noniwm, npH'IOMY M0 3aAOBOJibH51€ p5IA yMOB, ½Ki ¢opr,,iymo10TbCH HH)KY.e. 3oKpeMa, npH scix t E (0, T], u E { u: u E lR ;11 u II s M0 } npH KO)KHOMY i = l,n , s = 0, m + 1, nOBHHHa BHKOifYBaTHCb YMOBa sgn (A. ,(a5(t ), t, u) - a;(!)) = const # 0. Hexart ic1-1y 10Tb uesiA ' €MHi, cyMon11i Ha [O T] ¢ynKuii' A,(t) i F;(t), i = 1, 2, raKi, ll.(0 Mat\')Ke fl-JI½ ncix t E (0, 11 npH (X1, t, uO>), Cx2, t, u<2)) E D'Lo BHKOHYIOTbCH He- piBHOCTi I A.,(x1• t, u<1l)-A.,{t2, t, 1t<Zl)I 5 5 A1(t)lx1 -xz I+ Az(t)ll 11<1> - u(2) II , = Gi . (2) IJ;<x1, t, uO>)-/;V:2, t , u<2l) I 5 5 F1 U)l x 1 - x2 I+ F z(t) II 11°> - 1t<2> II, = Gi. EyJJ.eMo n0Marar11 raKO)K , mo6 A.1 s A.2 s .. . s A. 11 y DL0 , npH'lOMY ½Kll.(O AJIJI ,[J.e½KOT'O i E ( I , . . .. II - 1 } icHy€ XOY.a 6 OJ.J,Ha TO'-!Ka (xo, to) E QT TaKa, ll.(0 A;(xo, t0 , u(x0 , r0)) = A.;+ I(x0, t0 , u(x0, 10)). TO A,(x, t, u) = \+1(x, 1, u), (x, t, u.) E DL0 . fI03Ha'-!HMO '-1epe3 Au(L , 7) MeTpH'-IIIHA: npocrip HenepepBHHX <PYHKUiA: V ; QT ➔ lR " 3 piBHOMipHOIO MeTpHKOIO, JIKi 3a/1.0BOJibHjjl0Tb YMOBY Jlinwiua no X, I 3 KOHCTaHTOlO L 5IKl.l.(0 (x, I, V) E D'Lo, TO B CHJIY 3po6nem-1x BHl.l.(e nprmyll.(eHb B o6nacri Q T icny€ y3aranbnem-1R (no KapareotJ.opi [12, c . 194 - 199] po3s'H30K © I. 51. KM!Tb, 1993 ISSN 0041-6053 . YKp. Mam. )l(ypn .. 1993. m. 45. N• 9 1307 1308 I. 51. K.\--UTh m;('t; x, t, v) 3aAa'li d~ = -\(~. 't, v(~. 't)), ~(t) = X, VE Ao(L , n. d, (3) TI03I-Ia'IHMO qepe3 t,{t, t, v) HafiMenwe 3Ha'lemui 't [12. C. 194 - 195], npn RKOMY xapruuepncTHKa m,(,; x, t, v) nocRra€ rpairnui Q.T. Hexatt N - KiJihKiCTh xapaK­ TepHCTHK CHCTeMH ( 1), RKi npOXO!VITb qepe3 TO'IKH (ao(O), 0), (a,,,+ 1(0). 0 ) Ta 06J1aCTb 0.r. CttcTeMY (l) 6yneMO po3r J)j{)laTH 3 llO'laTKOBHMH YMOBaMH i = Gi. Ta YMOBaMH, j{Ki JaMiHIOIOTb rpaHH'fl·Ii na ~ Y,,.+1 : 11 m+l L L b,j,(t)u/a. (t), I) = h,{t), j =l s=O ne <p1(.x), b,js(t), h ,(t) - 1-1enepepsni rn J1inwiuesi 3 Konc-ramaMH <1> 1, B 1 llOBi)lHO, npH'IOMY (4) (5) HI BiH- Tip1mycn1.Mo TaKO)K ic1-1yBaJJHj{ TaKHx crai mx A 0 > 0, e0 E ] 0, minla0(t) - -am+1(t)I], ll.(0 He MeHwi Ao. TyT p - Kim,KiCTb xapaKTepHCTHK, 1.1(0 npOXO/lJ!Tb qepe3 TO'IKY (ao(O), 0) rn 06JiaCTb QT. ,[lJl.)f KO)KI-JOrO i = l. fl ll03Ha'fHMO qepe3 Q~; v , Q~-i v, Q;,;! I. I MHO)KHHlf TO'IOK (x, t) E Q, I.lJlR RKHX sinnoninno t,(r, t , v ) = 0; t1(r, t, v) > 0 m1(t1(r, t, v); x, t , v) = a0(11{t, t , v)); t1(t, t, v) > 0 m,<t,(1'., t, v); x, t , v ) = a,,,+1(t ,{x, t, v)). BooneMo ll(e AeHKi no311atJe1111H : = L p; v 1(1) = 111(a,,,+ 1(t).1) , i = n+p+l -N.11: B(t) = l bl JO ·· · blpO b,. 11+p+I-N. m+I · · · b l .11,111+1 ] l½10 . . . ½po½, 11 +p+I -N.m + l .. . h 2. 11 .111+ l .. . .. . .. ..... . . ..... .. ... ... ... ... ... .. hNw. • • bNpO bN .n+p+l-N.m+l • • . b N.11 .111+] rrp11nycKaio<111 np1-1 1~b0My. illO dctB "# 0. t E (0. T] . ISSN 004/ -6053. Yxp. Mam. ;,.;yp11., / 993. m . .J5 . N'' 9 TIPO O.UHY HEJIOKAJlbHY 3AllA '-IY .. . 1309 IliA y3ara.TibHeHHM po3B'R3K0M 3Ma'li (1), (4), (5) 6yAeM0 po3yMiTli JJinwiQeBli~ p03B' }130K CHCTervm iHTerpo-onepaTop,rnx piBH}IHb Ae npH'l0MY u,(x, t) = (R1u)(x, t) + t + J J,(w;('c; x. t, u), 't, u(w1(-r; x, t, u) , -r))d-r, - f.n . t,(x, ;, u) l<j);(W;(O; x, t, u)). (R,u)(1:, t) = µ 1(1,(x, t, u)), v,(t1(x, t, u)), (x, t) E n~t. (X, t) E nit, (X, t) E Q~1•:1, i• µ,(t) = Q,(t). i = [p, -----,--:-:--- v,(t) = Q1(t). i = n + p + 1- N. n , Q,(t) = I N [ 11 m _ -- L, B,lt) h/t) - L, L, bj1sCOQi(a/t), t) - det B(t) j = 1 1 = 1 , = 1 11 11+p-N ] L, b;1o(OQ1(aoU). t) - L, bj, 1, m+1(t)QiCam+1(t). t) , l=p+I i = I t Q1(x, t) = (R1u)(t, t) + J ft(w1(-r; x, t, u), 't, u)d't, t1(x. t , u) (6) (7) B jl• i, j = 1, N, - a11re6pai'l11i A0il0BHeHH}I BiAnOBiAHHX eneMeHTiB MaTpHQi B. O'leBHJ.lll0, LUO J.lJ(}I icnynamu1 y3araJi blleHoro p03B, }13KY He06XiI~HOIO € YM0Ba Y3- rOA)KeHOCTi 0-ro nop}IJ.lKy: 11 m+l L, L, b,j,(O)<p/a,(0)) = h1(0), = LN . j=l s=O Y npocrnpi A 0(L, T 1) (T1 E I 0. T]) po3rJ1>111eMo KyJ110 A(L,T1, M)={uE A0(L,T1): maxllu-<pll~M}, nT, He O < M ~ M0 - Cl>. To;d npH II E A (L, TI , M) MaeMo II u II ~ M + Cl> ~ M0 . (8) Il031Ul'lHMO 'lepe3 S onepaTop , 3aw11mll q)OpMyJiaMli ( 6) 11 BH3Ha'leimll Ha A (L, T1 , M). Tcopcr,m. Dpu ou,.;011m111i 6Cix 11pu11y111e11b, 3po6,1e11ux oi cJ1-1oc1m 3aiJa'li (I) . (4) : (5), ;I((}}/{//(/ (J/\(13{{n/l/ n/(1/\(! T1 E I OT]. llfO (3 n7i ic,1ye' €0111/llti y3ata1rb11e11ui1 p 0 3- o· Jl30/\ Lfiei° 3aOa'li , 11,.;11 i111a,1e)l{11mb A (L. T1• M ). j{oeeiJe1111Jl. TToKa)KeMo cnoYaTKY ic11y na1111H raK1-1x L. T I , LUO S nillo6pa)Ka€ KyJII0 A (L, T1. M) no1111oro MeTpH'IIIOI '() npocTopy B ce6e i € CTliCKyI0'lHM. ,llJl}I llbOl '0 BCTUH0BHM() J1inwi1teB iCTI, µ,(/) i V/i). B11Kop11CTOUYIO'IH (2). (3) Ta JleMy rpo11yOJ1J1a, 01\t'p)Kyt:MO = L,, ~ (9) ISSN 0041-6053. YKp. MOIi!. )l(ypu., 1993, m . .J5. N" 9 1310 I. 51. KMITb 1.1,e T, Q3 = f A.2 (1:)d1:. 0 Hexatt T I TaKe, w.o xapaKTepHCTHKli W;('t; a 1(T1), T 1, u(a I (T I ), T1)) i W;('t; a111(1' I ), T1,u(am(T1),T1)). i =Gi, 1.1,e UE A(L,Tl'M), nepernmUOTb t=O yMe)KaX n7i_ ToAi, BpaxosyIO'IH (6) - (9), V t1, t2 E [0, T1] OAep)Ky€MO max i=I, p, j=11+p+l-N, II Ae L 1 3a.Tle)KaTb BiA L, N, 11, m, \,J1, a1, bijs• h1, cp1, ½· Hexatt Tenep (x, t) E n 7i, u EA (L. T 1, M ). ToAi, spaxosy1o'IH (8), MaeMo IISu-cpll ~ (L 1 +<I> 1A+F)T1. BH6HpaIO'-IH Tenep T1 TaK, w.o6 BHKOHYBll.JIHCb nepimTOCTi mini am+1 (,)- aou) I AT1 ~ . ' 2 , AT1 ~ E0, JierKO OAep)Ky€MO, w.o 3a cniJibHY KOHCTUHTY Jlinwi1.1,a qlyuKqill Su no X MO)KHa npHfiHHTH max { L *, F + AL* ) , 1.1,e * ( - I L = Q 1 +LQ2 +max{<I>1,A0 (L 1 +F)})£, 7i Q, = f F, (1:)d1:, 0 i = 1,2; A0 = min A,, i=LJ A;*O T A1 ~ I 11.,{t, t, u) I, aoU) ~ x ~ ao(t) + Eo, t E [O, T], u E DM0 , A2 ~ I A;(\:, t , u) I, a111+1U) - qi ~ X ~ a111+1 (t), I E [0,Jl, UE D,i0 , i = n+p+l-N,n, A3 = min{la01, la:,i+11} I (A; He Bci piBHi 0). TaKHM '-IIHIOM, npH =Lp, L > max { max { <1> 1, ,:~,;/(L; + F)}, F + Amax { <1> 1, A.'cj1(L~ + F)}}, Ae L~ 3a.Tle)KHTb BiA N , n, m, 'A,; ,J;, bijs• h;, a;, cp1 i npH uocTaTHbO MaJIOMY 71 onepaTop S BiAo6pa)Ka€ A (L, T 1• M) B ce6e. ,llJIH Toro, w.06 s 6yJrO CTHCKYIO'IHM, HK HeBa)KKO nepesipHTH, 1.1,0CTanibO BHKO­ Ham1H nepiBHOCTefi - I (<1> 1 + Ao (L 1 + F) + Q 1 + LQz)EQ3 + Qz < 1. HKi 6yA)'Tb BHKOtlyBaTHCb npH l.l,OCTaTHbO MaJIOMY T1. ISSN 0041 -6053. YKp. ".am. )l(yp1t., 1993, m. 45. N• 9 nro OL(HY HEJIOKAJibHY 3AL(A '--IY ... 1311 31-IaXOA.H"'IHCb B YMOBax npm-11.1,Hny CTHCKYIO'IHX BiAo6pa:>KeHb, OAep:>Ky€M0 ueo6- XiAHe TBepA:>KeHH}I TeopeMH. 3ayeaJKe111tsi 1. Hexatt y, - rJiaAKi KpHBi, HKi 3aAOBOJibH.H"IOTb yM0BH: as(0) = = 0; as+ I (1) > a ,(t), 1 > 0. TOAi, p03r JIHAaJ0'IH 3aAa'ly (1). (5) B o6JiaCTi G, .H"Ka HBJIH€ COOOIO KpHBOJiittiA,rnA ceKT0p y sepx11iA niBnJIOI.L\HHi 1 > 0 n JIOI.L\HHH xOt, o6Me­ )KeHHA KpHBHMH Yo, Ym+I i npHMOI0 t = T, MO)KHa A0BeCTH amu10ri'IHY TeopeMY icHyBaJIH.H" TatglHIOCTi y3araJibHenoro po3B' R3KY. 2. 51.Kmo AO YMOBH icHyBaHIIR Ta €/{HIIOCTi y3ara.rihHeHoro p03B' .H"3KY AOAani AO­ AaTKOBY rJiaAKiCTb BHXiAHHX murnx 3aAa'li, a TaK0)K YMOBY y3roA:>KeHOCTi 1-ro no­ PRAKY. TO s TeopeMi po3B • H30K MO)KHa ssa:>KaTH KJiaCH'IHHM. Ue TsepA)KeHHR BiAHO­ CHThCH i AO 3aJJ,a'li (1), (5) 8 o6Jiacr; G. 3. HexaA BHKOHYIOTbCH YMOBH uaseAeHOI BHme TeopeMH. KpiM 1.1,bOro, Hexalt A; Ta f; , i = [,i, ne cnaAHi no x npH cpiKconaHHX t , u i He cnaAni no u np11 cpiK­ conamIx x, t. Ilp1myCTHM0 TaKO)K, mo KiJihKiCTb xapaKTepHCTHK, HKi BHXOARTb i3 TO'IOK (a0(0). 0) . (a,,.+ I (0). 0) i nonUAaion, B D.T, pisna n. HexaA npH U,bOMY f, ~ 0, i = = [p : /; ~ 0, i = p + L 11; tpyHKl~ii µ;, i = [p. - He cnaAHi, a V;, i = p + 1, n, - He 3p0CTalO'li. H exatt TaKO)K ic1-1y€ cyMOBHa Ha (0. T) Q)YHKU,iH 'If: JR +➔ JR +• AJIH RKOI j d-c 'lf(-C) a B Q Tx JR" BHKOliY€TbC.H" Hepim-,iCTb cpyHKU,iH M (t) i HenepepBHa HeCnaAHa = 00 1/;(r, t, 11) I ~ M (l)'lf(II u II). IlpH 1,Hx npHnymemui:x OAep:>KaHO pe3yJihTaT HeJIOKaJibHOI p038' H3yBaHOCTi po3- r JIHAysa1-1oi 3aAa'li. 1. llflUJ/llltllK E. 11. IlcKope KTHhle rpaHH'-!Hhle 33J.13'-IH ll/lJI nmpcpepeHLlH3Jll,HblX y pasHelrnll C '-!aCTHhlMH npoH3BOntlhlMH. - KHen: 1-l ayK. nyMKa, 1984. - 263 C. 2. K11p11A11~ 8 . M . H eK/laCCH '-leCK a JI 3ana'-la C HHTerpallbHhlMH 0 1·paHH'-ICHHJIMH /lJI JI nsyMepuoll nmep6oJIH'-ICCKOA Cl·ICTCMhl 11epnor·o nopllllK3 1/ B een,. JlbBOB. yn-Ta. Cep. MCX.· M3T. Bonpocbl MaT. aH3/IH3a Hero npI-111. - 1983. - 81,1n. 21. - C. 60- 64. 3. K11p11,111~ B . M . Onua 11eKJlaCCH '-ICCK3JI rpal-lH'-IH3JI 331!3'-la AII JI n11yMep110A r1-1nep6ol1 H'-ICCKOR CHCTCMbl ncpsoro 11 0pJIAK3 c pa3pI~BHhlMII K03<pq>Hl.lHCHTaMH // O61uaJ1 Tt:op1u1 rpaHH'-IHblX 3ana'-I: C6. 11ay'-!11. Tp. - K.11cn: HayK . nyMKa, 1983. -C. 267. 4. M eAblWK 3 . 0. O1111a HCKJI3CCH'-ICCKaJI rp3HH'-llla JI 33/13'-13 ll/l JI n111ep60J1H'-ICCKOR CHCTCMbl C IIBYMJI HC3aBHCHMhlMH 11epeMCllllblMH // }lmp<pcpe11L1. ypaBIICIIHJI. - 198 1. - 17, N"6. - C. 1096- 1104. 5. MeAbl<UK 3 . 0. 3a/)a'-la c l-1f1Ter·paJ1bHhlMl1 orpa1tl1'-ICHHJIMH /lJIJI nmep6om-l'-ICCKOl"O ypaBHC-HHJI BToporo nopJ111Ka // O6LuaJ1 -reop11J1 rpa111-I'-11tblX 3a11a'-I: Co. 11ay'-I . Tp. - K1-1cn: H3yK. IIYMKa, 1983. - C. 281 -282. 6. M eAbllllK 3 . 0. 3a11a'-la c H1tTc I·pam,11hlMH m ·paim'-ICIIHJIMH 11/IJI o61u11 x nsyMep111,1x nmcp6o­ Jrn'-ICCKHX ypas11e1111R H <.:HCTCM // 1l11¢¢epem1. ypaBHCI-IH>I . - 1985. - 21, N ° 2 . - C. 246 - 253. 7. M eAbllllK 3. 0., Kupu.111~ B. M . 3a11a'-la 6c3 Ha<!a/lbHhlX yc11o sI1A c HIITCrpaJ11, I11~M11 0 I ·p311H ­ '-l<'IIHJ1MH JlJl>I nmep60J11-l'-ICCKI-IX ypaBIIC IIHA 11a npllM0A // YKp. M,n. lKYP· - 1983 . - 35,N26 . - C. 722 - 727. 8. K ,,111/llb 11 . fl . () ll t: JI0KaJll,IIIJX Ja/la'-laX AJIJI rHncp60llfl'ICCKIIX CI-I CH'.M 11epsoro nop>1nKa . - Jlbnos, 199 1. - 54 c. - 1lC11 . n YKplHHnrrn, N °79- YK 91. 9. A6u.1111111 8 . 3., Mw11Kuc A . II. CMc111a1111a>1 3a/la'-!a n 1uI no'-ITH 111111cA11on 1·1-mcp60J11-1'-1ecKoA CI-ICTCMhl Ha rlJIOCK0 CTII // Ma, . co. - I 960. - 50, N °2 . - C. 423 - 442. 10. Mb1111Kuc A./(.. <Pu,11t.'"'"o" A . M . Ilc11pcp1rn111~c pc1ue1111J1 KBa3II.111-I11cf111IJX n-111cp0<>11H'-ICCK11x Cl·ICTCM C llllrtJI IIC3'1Bl·ICH~IIJ~III IIC[l<'MClllll~~lll // J\ l·l<plpCpt'llll, y palllll'IIHJI . - 1981. - t 1, N 3. - C. 488 - 5(1()_ 11. <P11.111 M01totJ A . M . JlocTaTO'-IIIIJC yc1IonI-I>1 1·.1106aJ11,11on pa3pc11IH~tllcHI CMcuIa11110A :i.tlla•rn /lllJI Klla3I·IJll·IIIClllllJX n111cp60Jll·l'll'CKIIX CIICTC~I C l lBY'IJI IIC3'1BIICH~l bl~II-I 11cpe~IClllll~MH. - M., 1980. - 17 c. -}le11. n BIIIIIITII , :'i"6-X I. 12. Epym11 II . Tl ., llf1110K<1.10 H . 3 .. fjo11,l<1p e1tKu II . C. It <lp . K y pc o6tJKIIOllt' llll!.X H1t<\ ll\>t'pt·11 - LlHaJ11,11IJx ypa1J1tc1111n. - K1-1c11: 81J111a 11IK .. 1974. -472 c Om·p>t<allO 17. m. ')2 ISSN 0041-6053 . .Yhp. MLJ/11, ;,;;_,,,,. ,, 1993. Ill. -15, N" 9 0121 0122 0123 0124 0125
id umjimathkievua-article-5934
institution Ukrains’kyi Matematychnyi Zhurnal
keywords_txt_mv keywords
language Ukrainian
English
last_indexed 2026-03-24T03:24:22Z
publishDate 1993
publisher Institute of Mathematics, NAS of Ukraine
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spelling umjimathkievua-article-59342020-03-19T09:21:13Z On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables Про одну нелокальну задачу для квазілінійної гіперболічної системи першого порядку з двома незалежними змінними Kmit, I. Ya. Кміть, І. Я. A mixed problem with nonlocal conditions on a space variable is considered for a system of quasilinear first-order hyperbolic equations with two independent variables. The sufficient conditions of solvability of this system are given. Для системи квазілінійних гіперболічних рівнянь першого порядку з двома незалежними змін­ними розглядається мішана задача, з нелокальними умовами по просторовій змінній. Наво­дяться достатні умови розв’язуваності. Institute of Mathematics, NAS of Ukraine 1993-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5934 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 9 (1993); 1307–1311 Український математичний журнал; Том 45 № 9 (1993); 1307–1311 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5934/8551 https://umj.imath.kiev.ua/index.php/umj/article/view/5934/8552 Copyright (c) 1993 Kmit I. Ya.
spellingShingle Kmit, I. Ya.
Кміть, І. Я.
On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title_alt Про одну нелокальну задачу для квазілінійної гіперболічної системи першого порядку з двома незалежними змінними
title_full On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title_fullStr On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title_full_unstemmed On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title_short On a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
title_sort on a nonlocal problem for a quasilinear first-order hyperbolic system with two independent variables
url https://umj.imath.kiev.ua/index.php/umj/article/view/5934
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