Abstract:
A problem of heat propagation in the ground from a heated pipeline with a partially heat-insulating shell is considered. The possibility is proved to construct a numerical solution of a linear heat equation by using a direct finite-difference method in the case when the thermal radiation on the ground surface is taken into account. On the basis of the theorem about the solvability of a system of linear difference equations by means of the sweep method, the existence and uniqueness of a solution of a corresponding difference problem with nonlinear boundary condition are proved.
Citation:
N. A. Vaganova, “Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 1, 2008, 11–21; Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S260–S271
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\by N.~A.~Vaganova
\paper Existence of a~solution of an initial-boundary value difference problem for a~linear heat equation with a~nonlinear boundary condition
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2008
\vol 14
\issue 1
\pages 11--21
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2008
\vol 261
\issue , suppl. 1
\pages S260--S271
\crossref{https://doi.org/10.1134/S0081543808050209}
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Linking options:
https://www.mathnet.ru/eng/timm3
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This publication is cited in the following 17 articles:
Mikhail Yu. Filimonov, Yaroslav K. Kamnev, Aleksandr N. Shein, Nataliia A. Vaganova, “Modeling the Temperature Field in Frozen Soil under Buildings in the City of Salekhard Taking into Account Temperature Monitoring”, Land, 11:7 (2022), 1102
N. A. Vaganova, M. Yu. Filimonov, THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020), 2337, THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020), 2021, 090011
N. A. Vaganova, M. Yu. Filimonov, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2312, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2020, 050026
V. V. Makhneva, N. A. Vaganova, M. Yu. Filimonov, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2312, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2020, 050013
M. Yu. Filimonov, N. A. Vaganova, Lecture Notes in Computer Science, 11386, Finite Difference Methods. Theory and Applications, 2019, 233
N. A. Vaganova, M. Yu. Filimonov, Lecture Notes in Computer Science, 11386, Finite Difference Methods. Theory and Applications, 2019, 580
M Yu Filimonov, “Representation of solutions of boundary value problems for nonlinear evolution equations by special series with recurrently calculated coefficients”, J. Phys.: Conf. Ser., 1268:1 (2019), 012071
Vaganova N.A., “Simulation of Thermal Stabilization of Bases Under Engineering Structures in Permafrost Zone”, AIP Conference Proceedings, 2048, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2018, 030010
M Yu Filimonov, N A Vaganova, “Flare Systems Exploitation and Impact on Permafrost”, J. Phys.: Conf. Ser., 899:9 (2017), 092004
Vaganova N., Filimonov M.Yu., “Different Shapes of Constructions and Their Effects on Permafrost”, Applications of Mathematics in Engineering and Economics (AMEE'16), AIP Conference Proceedings, 1789, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2016, UNSP 020019
M Yu Filimonov, N A Vaganova, “Simulation of permafrost changes due to technogenic influences of different ingeneering constructions used in nothern oil and gas fields”, J. Phys.: Conf. Ser., 754 (2016), 112004
M Filimonov, A Masih, “Presentation of special series with computed recurrently coefficients of solutions of nonlinear evolution equations”, J. Phys.: Conf. Ser., 722 (2016), 012040
M. Yu. Filimonov, N. A. Vaganova, Lecture Notes in Computer Science, 9045, Finite Difference Methods,Theory and Applications, 2015, 185
N. A. Vaganova, M. Yu. Filimonov, AIP Conference Proceedings, 1690, 2015, 020016
A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215
N. A. Vaganova, M. Yu. Filimonov, “Modelirovanie ekspluatatsii inzhenernykh sistem v usloviyakh vechnoi merzloty”, Vestn. NGU. Ser. matem., mekh., inform., 13:4 (2013), 37–42
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