Abstract:
We obtain the fundamental solution for an equation of the third order with multiple characteristics using the construction of self-similar solution.
Received 22.02.2007
Document Type:
Article
UDC:517.956
Language: Russian
Citation:
T. D. Dzhuraev, Yu. P. Apakov, “On self-similar solution of an equation of the third order with multiple characteristics”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(15) (2007), 18–26
\Bibitem{DzhApa07}
\by T.~D.~Dzhuraev, Yu.~P.~Apakov
\paper On self-similar solution of an equation of the third order with multiple characteristics
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2007
\vol 2(15)
\pages 18--26
\mathnet{http://mi.mathnet.ru/vsgtu525}
\crossref{https://doi.org/10.14498/vsgtu525}
Linking options:
https://www.mathnet.ru/eng/vsgtu525
https://www.mathnet.ru/eng/vsgtu/v115/p18
This publication is cited in the following 23 articles:
B. Y. Irgashev, “Application of hypergeometric functions to the construction of particular solutions”, Complex Variables and Elliptic Equations, 2023, 1
Yu. P. Apakov, R. A. Umarov, “Construction of the Solution of a Boundary-Value Problem for the Third-Order Equation with Lower Terms with the Help of the Green Function”, J Math Sci, 274:6 (2023), 807
Yu. P. Apakov, A. A. Hamitov, “On solution of the boundary value problems posed for an equation with the third-order multiple characteristics in semi-bounded domains in three dimensional space”, Bol. Soc. Mat. Mex., 29:3 (2023)
Yusupzhon Apakov, Azizbek Khamitov, “O RAZREShIMOSTI KRAEVOI ZADAChI DLYa URAVNENIYa TRETEGO PORYaDKA S KRATNYMI KhARAKTERISTIKAMI V TREKhMERNOM PROSTRANSTVE V POLUOGRANIChENNOI OBLASTI”, VOGUMFT, 2023, no. 1 (2), 13
B. Yu. Irgashev, “Construction of Fundamental Solution for an Odd-Order Equation”, Vestnik St.Petersb. Univ.Math., 56:4 (2023), 512
Irgashev B.Y., “Particular Solutions of Equations With Multiple Characteristics Expressed Through Hypergeometric Functions”, Georgian Math. J., 29:2 (2022), 211–224
E. Yu. Grazhdantseva, “O tochnom reshenii giperbolicheskoi sistemy differentsialnykh uravnenii”, Vestnik rossiiskikh universitetov. Matematika, 27:140 (2022), 328–338
Yuldashev T.K., Apakov Yu.P., Zhuraev A.Kh., “Boundary Value Problem For Third Order Partial Integro-Differential Equation With a Degenerate Kernel”, Lobachevskii J. Math., 42:6, SI (2021), 1317–1327
Apakov Yu.P., “on Unique Solvability of a Boundary-Value Problem For a Viscous Transonic Equation”, Lobachevskii J. Math., 41:9, SI (2020), 1754–1761
Irgashev B.Yu., “Construction of Singular Particular Solutions Expressed Via Hypergeometric Functions For An Equation With Multiple Characteristics”, Differ. Equ., 56:3 (2020), 315–323
Apakov Yu.P., Zhuraev A.Kh., “Third Boundary-Value Problem For a Third-Order Differential Equation With Multiple Characteristics”, Ukr. Math. J., 70:9 (2019), 1467–1476
B. Yu. Irgashev, “On Partial Solutions of One Equation with Multiple Characteristics and Some Properties of the Fundamental Solution”, Ukr. Math. J., 68:6 (2016), 868–893
Zh. A. Balkizov, “Kraevaya zadacha dlya uravneniya tretego poryadka s kratnymi kharakteristikami”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 17:3 (2015), 13–21
Apakov Yu.P., Irgashev B.Yu., “Boundary-Value Problem For a Degenerate High-Odd-Order Equation”, Ukr. Math. J., 66:10 (2015), 1475–1490
T. K. Yuldashev, “Obratnaya zadacha dlya odnogo integro-differentsialnogo uravneniya Fredgolma v chastnykh proizvodnykh tretego poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(34) (2014), 56–65
V. V. Shubin, “Boundary value problems for third-order equations with discontinuous coefficient”, J. Math. Sci., 198:5 (2014), 637–647
Yu. P. Apakov, “On the solution of a boundary-value problem for a third-order equation with multiple characteristics”, Ukr. Math. J., 64:1 (2012), 1–12
G. A. Lukina, “Kraevye zadachi s integralnymi granichnymi usloviyami dlya linearizovannogo uravneniya Kortevega–de Friza”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 8, 52–61
V. V. Shubin, “Vesovye otsenki resheniya nekotorykh zadach dlya uravneniya tretego poryadka s razryvnym koeffitsientom”, Matematicheskie zametki SVFU, 18:2 (2011), 218–228
F. M. Fedorov, “K teorii gaussovykh beskonechnykh sistem lineinykh algebraicheskikh uravnenii (BSLAU)”, Matematicheskie zametki SVFU, 18:2 (2011), 209–217
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