Abstract:
In work necessary and sufficient conditions of uniqueness of the decision of a regional problem for the loaded equation mixed parabolic hyperbolic type in rectangular area are established. The problem decision is constructed in the form of the number sum on own functions of a corresponding one-dimensional problem on own values.
Keywords:
loaded equation of mixed type, spectral method, uniqueness, existence.
Original article submitted 01/IX/2010 revision submitted – 11/X/2010
Citation:
A. V. Tarasenko, “The Boundary Value Problem for the Loaded Equation of Mixed Parabolic-Hyperbolic Type in Rectangular Area”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 5(21) (2010), 263–267
\Bibitem{Tar10}
\by A.~V.~Tarasenko
\paper The Boundary Value Problem for the Loaded Equation of Mixed Parabolic-Hyperbolic Type in~Rectangular Area
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2010
\vol 5(21)
\pages 263--267
\mathnet{http://mi.mathnet.ru/vsgtu825}
\crossref{https://doi.org/10.14498/vsgtu825}
Linking options:
https://www.mathnet.ru/eng/vsgtu825
https://www.mathnet.ru/eng/vsgtu/v121/p263
This publication is cited in the following 6 articles:
A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov ATλ,j”, Izv. vuzov. Matem., 2024, no. 2, 59–80
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators ATλ,j”, Russ Math., 68:2 (2024), 52
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators ATλ,j”, Izv. Math., 87:6 (2023), 1227–1254
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
A. K. Urinov, E. T. Karimov, S. Kerbal, “Kraevaya zadacha s integralnym usloviem sopryazheniya dlya uravneniya v chastnykh proizvodnykh s drobnoi proizvodnoi Rimana—Liuvillya, svyazannaya s techeniem gaza v kanale, okruzhennom poristoi sredoi”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 66–76
I. G. Mamedov, “Trekhmernaya integro-mnogotochechnaya kraevaya zadacha dlya nagruzhennykh volterro-giperbolicheskikh integro-differentsialnykh uravnenii tipa Bianki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(26) (2012), 8–20
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