Geodesic
Classical solutions of mixed problems for a one-dimensional wave equation in the class of smooth high-order functions
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 32-39.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, the classical solutions of the first and second mixed problems for a one-dimensional wave equation are studied. These problems are considered in the class of continuously differentiable functions of order greater than two. The classical solutions of the problems posed are obtained in an analytical form. The uniqueness of the solutions found is proved. 
@article{TIMB_2020_28_1_a3,
     author = {V. I. Korzyuk and I. S. Kozlovskaja and S. N. Naumavets},
     title = {Classical solutions of mixed problems for a one-dimensional wave equation in the class of smooth high-order functions},
     journal = {Trudy Instituta matematiki},
     pages = {32--39},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a3/}
}
TY  - JOUR
AU  - V. I. Korzyuk
AU  - I. S. Kozlovskaja
AU  - S. N. Naumavets
TI  - Classical solutions of mixed problems for a one-dimensional wave equation in the class of smooth high-order functions
JO  - Trudy Instituta matematiki
PY  - 2020
SP  - 32
EP  - 39
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a3/
LA  - ru
ID  - TIMB_2020_28_1_a3
ER  - 
%0 Journal Article
%A V. I. Korzyuk
%A I. S. Kozlovskaja
%A S. N. Naumavets
%T Classical solutions of mixed problems for a one-dimensional wave equation in the class of smooth high-order functions
%J Trudy Instituta matematiki
%D 2020
%P 32-39
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a3/
%G ru
%F TIMB_2020_28_1_a3
V. I. Korzyuk; I. S. Kozlovskaja; S. N. Naumavets. Classical solutions of mixed problems for a one-dimensional wave equation in the class of smooth high-order functions. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 32-39. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a3/

[1] Baranovskaya S. N., Yurchuk N. I., “Smeshannaya zadacha dlya uravneniya kolebaniya struny s zavisyaschei ot vremeni kosoi proizvodnoi v kraevom uslovii”, Differentsialnye uravneniya, 45:8 (2009), 1188–1191 | MR | Zbl

[2] Korzyuk V. I., Cheb E. S., Shirma M. S., “Reshenie pervoi smeshannoi zadachi dlya volnovogo uravneniya metodom kharakteristik”, Trudy Instituta matematiki, 17:2 (2009), 23–24

[3] Korzyuk V. I., Cheb E. S., Karpechina A. A., “Klassicheskoe reshenie pervoi smeshannoi zadachi v polupolose dlya lineinogo giperbolicheskogo uravneniya vtorogo poryadka”, Trudy Instituta matematiki, 20:2 (2012), 64–74 | MR | Zbl

[4] Korzyuk V. I., Kozlovskaya I. S., “Ob usloviyakh soglasovaniya v granichnykh zadachakh dlya giperbolicheskikh uravnenii”, Dokl. NAN Belarusi, 57:5 (2013), 37–42 | MR | Zbl

[5] Korzyuk V. I., Kozlovskaya I. S., Naumovets S. N., “Klassicheskoe reshenie pervoi smeshannoi zadachi odnomernogo volnovogo uravneniya s usloviyami tipa Koshi”, Ves. Nats. akad. navuk Belarusi. Ser. fiz.-mat. navuk, 2015, no. 1, 7–20

[6] Korzyuk V. I., Naumovets S. N., Kozlovskaya I. S., “Klassicheskie resheniya v teorii differentsialnykh uravnenii s chastnymi proizvodnymi”, Studia i materialy Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie, 2015, no. 1(9), 55–78

[7] Korzyuk V. I., Naumovets S. N., “Klassicheskoe reshenie smeshannoi zadachi dlya odnomernogo volnovogo uravneniya s proizvodnymi vysokogo poryadka v granichnykh usloviyakh”, Dokl. NAN Belarusi, 60:3 (2016), 11–17 | MR | Zbl

[8] Korzyuk V. I., “Metod kharakteristicheskogo parallelogramma na pri-mere pervoi smeshannoi zadachi dlya odnomernogo volnovogo uravneniya”, Dokl. NAN Belarusi, 61:3 (2017), 7–13 | MR | Zbl

[9] Korzyuk V. I., Naumovets S. N., Sevostyuk V. A., “O klassicheskom reshenii vtoroi smeshannoi zadachi dlya odnomernogo volnovogo uravneniya”, Trudy Instituta matematiki, 26:1 (2018), 35–42

[10] Korzyuk V. I., Naumovets S. N., Serikov V. P., “Metod kharakteristicheskogo parallelogramma resheniya vtoroi smeshannoi zadachi dlya odnomernogo volnovogo uravneniya”, Trudy Instituta matematiki, 26:1 (2018), 43–53

[11] Moiseev E. I., Korzyuk V. I., Kozlovskaya I. S., “Klassicheskoe reshenie zadachi s integralnym usloviem dlya odnomernogo volnovogo uravneniya”, Differentsialnye uravneniya, 50:10 (2014), 1373–1385 | DOI | Zbl

[12] Korzyuk V. I., Naumovets S. N., Kozlovskaya I. S., “Klassicheskoe reshenie zadachi dlya odnomernogo volnovogo uravneniya s integralnymi usloviyami vtorogo roda”, Differentsialnye uravneniya, 55:3 (2019), 353–362 | DOI | MR | Zbl

[13] Moiseev E. I., Lomovtsev F. E., Novikov E. N., “Neodnorodnoe faktorizovannoe giperbolicheskoe uravnenie vtorogo poryadka v chetverti ploskosti pri polunestatsionarnoi vtoroi kosoi proivodnoi v granichnom uslovii”, Dokl. Rossiiskoi akademii nauk, 459:5 (2014), 544–549 | DOI | Zbl

[14] Lomovtsev F. E., Novikov E. N., “Neobkhodimye i dostatochnye usloviya kolebanii ogranichennoi struny pri kosykh proizvodnykh v granichnykh usloviyakh”, Differentsialnye uravneniya, 50:1 (2014), 126–129 | DOI | Zbl

[15] Korzyuk V. I., Kozlovskaya I. S., Klassicheskie resheniya zadach dlya giperbolicheskikh uravnenii, V desyati chastyakh, v. 1, Minsk, 2017, 45 pp.

[16] Korzyuk V. I., Kozlovskaya I. S., Klassicheskie resheniya zadach dlya giperbolicheskikh uravnenii, V desyati chastyakh, v. 2, Minsk, 2017, 52 pp.

[17] Korzyuk V. I., Mandrik A. A., “Pervaya smeshannaya zadachi dlya nestrogo giperbolicheskogo uravneniya tretego poryadka v zamknutoi oblasti”, Differentsialnye uravneniya, 52:6 (2016), 788–802 | DOI | Zbl

[18] Korzyuk V. I., Mandrik A. A., “Pervaya smeshannaya zadacha v polupolose dlya neodnorodnogo nestrogo giperbolicheskogo uravneniya tretego poryadka”, Ves. Nats. akad. navuk Belarusi. Ser. fiz.-mat. navuk, 2015, no. 4, 10–17