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@article{TIMB_2010_18_2_a2, author = {V. I. Korzyuk and I. S. Kozlovskaya}, title = {Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of {time.~I}}, journal = {Trudy Instituta matematiki}, pages = {22--35}, publisher = {mathdoc}, volume = {18}, number = {2}, year = {2010}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a2/} }
TY - JOUR AU - V. I. Korzyuk AU - I. S. Kozlovskaya TI - Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of time.~I JO - Trudy Instituta matematiki PY - 2010 SP - 22 EP - 35 VL - 18 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a2/ LA - ru ID - TIMB_2010_18_2_a2 ER -
%0 Journal Article %A V. I. Korzyuk %A I. S. Kozlovskaya %T Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of time.~I %J Trudy Instituta matematiki %D 2010 %P 22-35 %V 18 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a2/ %G ru %F TIMB_2010_18_2_a2
V. I. Korzyuk; I. S. Kozlovskaya. Two-point boundary problem for string oscillation equationwith given velocity in arbitrary point of time.~I. Trudy Instituta matematiki, Tome 18 (2010) no. 2, pp. 22-35. http://geodesic.mathdoc.fr/item/TIMB_2010_18_2_a2/
[1] Korzyuk V.I., Cheb E.S., Shirma M.S., “Klassicheskoe reshenie pervoi smeshannoi zadachi dlya uravneniya kolebaniya struny”, Dokl. NAN Belarusi, 53:1 (2008), 45–49 | MR
[2] Korzyuk V.I., Cheb E.S., Shirma M.S., “Reshenie pervoi smeshannoi zadachi dlya volnovogo uravneniya metodom kharakteristik”, Tr. Instituta matematiki, 17:2 (2009), 23–34
[3] Aleksandryan R.A., i dr., Differentsialnye uravneniya s chastnymi proizvodnymi, Nauka, M., 1970 | MR | Zbl
[4] Antonevich A.B., “Dvukhtochechnaya zadacha dlya uravneniya kolebanii struny i svyazannye s nei funktsionalnye uravneniya”, Differents. uravneniya, 21:3 (1985), 426–434 | MR
[5] Berezanskii Yu.M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Kiev, 1965
[6] Vakhaniya N.N., “Ob odnoi kraevoi zadache s zadaniem na vsei granitse dlya giperbolicheskoi sistemy, ekvivalentnoi uravneniyu kolebaniya struny”, Dokl. AN SSSR, 116:6 (1957), 906–909 | Zbl
[7] Sobolev S.L., “Primer korrektnoi kraevoi zadachi dlya uravneniya kolebanii struny s dannymi na vsei granitse”, Dokl. AN SSSR, 109:4 (1956), 707–709 | MR | Zbl
[8] Bernik V.I., Ptashnik B.I., Salyga B.O., “Analog mnogosetochnoi zadachi dlya giperbolicheskogo uravneniya s postoyannymi koeffitsientami”, Differents. uravneniya, 13:4 (1977), 637–645 | MR | Zbl
[9] Gordeziani D.G., Avalishvili G.A., “Reshenie nelokalnykh zadach dlya odnomernykh kolebanii sredy”, Matematicheskoe modelirovanie, 12:1 (2000), 94–103 | MR | Zbl
[10] Ilin V.A., “Analiticheskii vid optimalnogo granichnogo upravleniya smescheniem na odnom kontse struny s modelnym nelokalnym granichnym usloviem odnogo iz chetyrekh tipov”, Dokl. AN, 420:3 (2008), 309–313 | MR
[11] Ilin V.A., “Optimizatsiya granichnogo upravleniya uprugoi siloi na odnom kontse struny s modelnym nelokalnym granichnym usloviem odnogo iz chetyrekh tipov”, Dokl. RAN, 420:4 (2008), 442–446
[12] Ilin V.A., “O nezavisimosti optimalnykh granichnykh upravlenii kolebaniyami struny ot vybora tochki soglasovaniya nachalnykh i finalnykh uslovii”, Differents. uravneniya, 44:3 (2008), 383–389 | MR
[13] Ilin V.A., “Edinstvennost obobschennykh reshenii smeshannykh zadach dlya volnovogo uravneniya s nelokalnymi granichnymi usloviyami”, Differents. uravneniya, 44:5 (2008), 672–680 | MR
[14] Ilin V.A., Moiseev E.I., “Optimizatsiya granichnykh upravlenii kolebaniyami struny”, Uspekhi matematicheskikh nauk, 60:6(366) (2005), 89–114 | MR
[15] Ilin V.A., Moiseev E.I., “Optimalnoe granichnoe upravlenie smescheniem na odnom kontse struny pri svobodnom vtorom ee kontse za lyuboi dostatochno bolshoi promezhutok vremeni”, Differents. uravneniya, 43:10 (2007), 1369–1381 | MR
[16] Ilin V.A., Moiseev E.I., “Optimizatsiya za proizvolnyi dostatochno bolshoi promezhutok vremeni granichnykh upravlenii smescheniyami na dvukh kontsakh struny”, Differents. uravneniya, 43:11 (2007), 1528–1544 | MR
[17] Ilin V.A., Moiseev E.I., “Optimalnoe granichnoe upravlenie uprugoi siloi na odnom kontse struny pri svobodnom vtorom ee kontse za proizvolnyi dostatochno bolshoi promezhutok vremeni”, Differents. uravneniya, 43:12 (2007), 1655–1663 | MR
[18] Ilin V.A., Moiseev E.I., “Optimizatsiya upravleniya na dvukh kontsakh struny uprugimi granichnymi silami za lyuboi dostatochno bolshoi promezhutok vremeni”, Differents. uravneniya, 44:1 (2008), 89–110 | MR
[19] Korzyuk V.I., Erofeenko V.T., Pulko Yu.V., “Klassicheskoe reshenie nachalno-kraevoi zadachi dlya volnovogo uravneniya s integralnym po vremeni granichnym usloviem”, Dokl. NAN Belarusi, 82:5 (2009), 36–41 | MR
[20] Polischuk V.N., “Zadacha s nelokalnymi kraevymi usloviyami dlya giperbolicheskikh uravnenii s peremennymi koeffitsientami”, Priblizhennye i kachestvennye metody teorii differentsialnykh i differentsialno-funktsionalnykh uravnenii, In-t mat. AN USSR, Kiev, 1979, 54–64
[21] Ptashnik B.I., Nekorrektnye granichnye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi, Nauk. dumka, Kiev, 1984 | MR
[22] Pulkina L.S., “Smeshannaya zadacha s integralnym usloviem dlya giperbolicheskogo uravneniya”, Matematicheskie zametki, 74:3 (2003), 435–445 | MR
[23] Pulkina L.S., “Nelokalnaya zadacha s integralnymi usloviyami dlya giperbolicheskogo uravneniya”, Differents. uravneniya, 40:7 (2004), 887–892 | MR
[24] Pulkina L.S., “Nelokalnaya zadacha s integralnym usloviem pervogo roda dlya mnogomernogo giperbolicheskogo uravneniya”, Dokl. RAN, 416:5 (2007), 597–599 | MR
[25] Pulkina L.S., Kozhanov A.I., “Kraevye zadachi s integralnym granichnym usloviem dlya mnogomernykh giperbolicheskikh uravnenii”, Dokl. RAN, 404:5 (2005), 589–592 | MR
[26] Slobodetskii L.N., “Obobschennye prostranstva Soboleva i ikh prilozheniya k kraevym zadacham dlya differentsialnykh uravnenii v chastnykh proizvodnykh”, Uch. zap. Leningr. ped. in-ta im. A.I. Gertsena, 197, 1958, 54–112
[27] Stein Ilaies M., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR
[28] Whitney H., “Analytic extensions of differentiable functions defined in closed sets”, Trans. Amer. Math. Soc., 36 (1934), 63–89 | DOI | MR