Geodesic
Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 1, pp. 11-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 1, pp. 11-21. http://geodesic.mathdoc.fr/item/TIMM_2008_14_1_a1/

[1] Budadin O. N., Potapov A. I. i dr., Teplovoi nerazrushayuschii kontrol izdelii, Nauka, M., 2002

[2] Quitner P., “Global existence of solutions of parabolic problems with nonlinear boundary conditions”, Singularities and differential equations, 33, Banach center publications, Warszawa, 1996, 309–314 | MR

[3] Titov S. S., “Reshenie periodicheskikh zadach Koshi s pomoschyu spetsialnykh trigonometricheskikh ryadov”, Chislennye metody mekhaniki sploshnoi sredy, 9:2 (1984), 112–124 | MR

[4] Cherepanov A. N., Shapeev V. P., Fomin V. M., Semin L. G., “Chislennoe modelirovanie teplofizicheskikh protsessov pri lazerno-luchevoi svarke s obrazovaniem parovogo kanala”, Prikl. mekhanika i tekhn. fizika, 47:5 (2006), 88–96 | MR | Zbl

[5] Shapeev V. P., Cherepanov A. N., “Konechno-raznostnyi algoritm dlya chislennogo modelirovaniya protsessov lazernoi svarki metallicheskikh plastin”, Vychisl. tekhnologii, 11:4 (2006), 102–117

[6] Kovenya V. M., Yanenko N. N., Metod rasschepleniya v zadachakh gazovoi dinamiki, Nauka, Novosibirsk, 1981 | MR | Zbl

[7] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[8] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1992 | MR

[9] Vaganova N. A., “Modelirovanie neodnorodnykh teplovykh polei ot zaglublennogo istochnika na dnevnoi poverkhnosti”, Cb. nauch. tr., Matematicheskoe i informatsionnoe modelirovanie, 7, Vektor Buk, Tyumen, 2005, 77–84