О КРИТЕРИИ ГЛАДКОСТИ КЛАССИЧЕСКОГО РЕШЕНИЯ НЕОДНОРОДНОГО МОДЕЛЬНОГО ТЕЛЕГРАФНОГО УРАВНЕНИЯ В ПЕРВОЙ ЧЕТВЕРТИ ПЛОСКОСТИ

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Ф. Е. ЛОМОВЦЕВ

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ЛОМОВЦЕВ, Ф. Е. (2023). О КРИТЕРИИ ГЛАДКОСТИ КЛАССИЧЕСКОГО РЕШЕНИЯ НЕОДНОРОДНОГО МОДЕЛЬНОГО ТЕЛЕГРАФНОГО УРАВНЕНИЯ В ПЕРВОЙ ЧЕТВЕРТИ ПЛОСКОСТИ. Вестник Полоцкого государственного университета. Серия С. Фундаментальные науки, (1), 72-83. https://doi.org/10.52928/2070-1624-2023-40-1-72-83
Биография автора

Ф. Е. ЛОМОВЦЕВ, Белорусский государственный университет, Минск

д-р физ.-мат. наук, проф.

Библиографические ссылки

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.).

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