ON THE SMOOTHNESS CRITERION FOR A CLASSICAL SOLUTION TO AN INHOMOGENEOUS MODEL TELEGRAPH EQUATION IN THE FIRST QUARTER OF THE PLANE

Main Article Content

F. LOMOVTSEV

Abstract

Article Details

How to Cite
LOMOVTSEV, F. (2023). ON THE SMOOTHNESS CRITERION FOR A CLASSICAL SOLUTION TO AN INHOMOGENEOUS MODEL TELEGRAPH EQUATION IN THE FIRST QUARTER OF THE PLANE. Vestnik of Polotsk State University. Part C. Fundamental Sciences, (1), 72-83. https://doi.org/10.52928/2070-1624-2023-40-1-72-83
Section
mathematics
Author Biography

F. LOMOVTSEV, Belarusian State University, Minsk

д-р физ.-мат. наук, проф.

References

Lomovtsev, F. E. (2022). Kriteriy gladkosti klassicheskogo resheniya neodnorodnogo model'nogo telegrafnogo uravneniya pri skorosti a(x,t) na poluosi [The Smoothness Criterion for the Classical Solution to Inhomogeneous Model Telegraph Equation at the Rate a(x,t) on the Half-Line]. In Trudy 10-go mezhdunarodnogo nauchnogo seminara AMADE-2021 [Proc. 10th International Workshop AMADE-2021] (43–53). Minsk: BSU, ITC of the Ministry of Finance. (In Russ.).

Lomovtsev, F. E. (2022). Kriterii gladkosti chastnogo klassicheskogo resheniya neodnorodnogo model'nogo telegrafnogo uravneniya v pervoi chetverti ploskosti [Smoothness Criterion for a Particular Classical Solution of an Inhomogeneous Model Telegraph Equation in the First Quarter of the Plane]. Vestnik Polotskogo gosudarstvennogo universiteta. Seriya C, Fundamental'nye nauki [Herald of Polotsk State University. Series С. Fundamental sciences], (11), 99–116. DOI: 10.52928/2070-1624-2022-39-11-99-116. (In Russ., abstr. in Engl.).

Lomovtsev, F. E. (2017). Metod korrektirovki probnogo resheniya obshchego volnovogo uravneniya v pervoi chetverti ploskosti dlya minimal'noi gladkosti ego pravoi chasti [Correction method of test solutions of the general wave equation in the first quarter of the plane for the minimum smoothness of its right-hand side]. Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika [J. of the Belarusian State University. Mathematics and informatics], (3), 38–52. (In Russ., abstr. in Engl.).

Lomovtsev, F. E. (2021). V krivolineinoi pervoi chetverti ploskosti metod korrektirovki probnykh reshenii dlya minimal'noi gladkosti pravoi chasti volnovogo uravneniya s postoyannymi koeffitsientami [In the curvilinear first quarter of the plane the correction method of test solutions for the minimum smoothness of the right-hand side for the wave equation with constant coefficients]. Vesnik Vitsebskaga dzyarzhaunaga universiteta [J. of Vitebsk State University], 4(113), 5–22. (In Russ., abstr. in Engl.).

Lomovtsev, F. E. (2021). Pervaya smeshannaya zadacha dlya obshchego telegrafnogo uravneniya s peremennymi koeffitsientami na polupryamoi [The first mixed problem for the general telegraph equation with variable coefficients on the half-line]. Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika [J. of the Belarusian State University. Mathematics and informatics], (1), 18–38. (In Russ., abstr. in Engl.).

Lomovtsev, F. E., & Ustilko, E. V. (2020). Smeshannaya zadacha dlya odnomernogo volnovogo uravneniya pri kharakteristicheskoi pervoi kosoi proizvodnoi v nestatsionarnom granichnom rezhime dlya gladkikh reshenii [A mixed problem for a one-dimensional wave equation with a characteristic first oblique derivative in a non-stationary boundary regime for smooth solutions]. Vesnik Magileuskaga dzyarzhaunaga universiteta imya A. A. Kulyashova. Ser B. Pryrodaznauchyya navuki [Mogilev State A. Kuleshov Bulletin. Series B. Natural Sciences], 2(56), 21–36. (In Russ., abstr. in Engl.).

Lomovtsev, F. E., & Lysenko, V. V. (2021). Smeshannaya zadacha dlya obshchego odnomernogo volnovogo uravneniya v polupolose ploskosti pri nestatsionarnykh nekharakteristicheskikh vtorykh proizvodnykh [A mixed problem for a general one-dimensional wave equation in a half-strip of the plane with non-stationary non-characteristic second derivatives]. Vesnik Magileuskaga dzyarzhaunaga universiteta imya A. A. Kulyashova. Ser B. Pryrodaznauchyya navuki [Mogilev State A. Kuleshov Bulletin. Series B. Natural Sciences], 2(58), 28–54. (In Russ., abstr. in Engl.).

Lomovtsev, F. E., & Spesivtseva, K. A. (2021). Mixed Problem for a General 1D Wave Equation with Characteristic Second Derivatives in a Nonstationary Boundary Mode. Math Notes, 110(3), 329–338. DOI: 10.1134/S0001434621090030.

Khromov, A. P., & Kornev, V. V. (2019). Klassicheskoe i obobshchennoe resheniya smeshannoi zadachi dlya neodnorodnogo volnovogo uravneniya [Classical and generalized solutions of a mixed problem for a non-homogeneous wave equation]. Doklady Akademii nauk, 484(1), 18–20. DOI: 10.31857/S0869-5652484118-20.

Khromov, A. P. (2019). Neobkhodimye i dostatochnye usloviya sushchestvovaniya klassicheskogo resheniya smeshannoi zadachi dlya odnorodnogo volnovogo uravneniya v sluchae summiruemogo potentsiala [Necessary and sufficient conditions for the existence of a classical solution of the mixed problem for the homogeneous wave equation with an integrable potential]. Differentsial'nye uravneniya [Differential equations], 55(5), 703–717. DOI: 10.1134/S0012266119050112.

Khromov, A. P. (2022). Raskhodyashchiesya ryady i obobshchennaya smeshannaya zadacha dlya volnovogo uravneniya [Divergent series and generalized mixed problem for wave equation]. In Sovremennye problemy teorii funktsii i ikhprilozheniya: vyp. 21 [Modern problems of the theory of functions and their applications: iss. 21] (319–324). Saratov: Saratov State University. (In Russ., abstr. in Engl.).

Lomov, I. S. (2022). Construction of a generalized solution of a mixed problem for the telegraph equation: sequential and axiomatic approaches. Differential equations, 58(11), 1468–1481. DOI: 10.1134/S00122661220110040.

Tikhonov, A. N., & Samarskii, A. A. (2004). Uravneniya matematicheskoi fiziki. Moscow: Nauka. (In Russ.).