Geodesic
Study of steady-state heat distribution in a plane with a crack in the case of variable internal thermal conductivity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 695-703 
A. V. Glushko; E. A. Loginova; V. E. Petrova; A. S. Ryabenko. Study of steady-state heat distribution in a plane with a crack in the case of variable internal thermal conductivity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 695-703. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a15/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The existence of a solution to the problem modeling a steady-state heat distribution in an inhomogeneous plane with a crack is proved. The singular terms of an asymptotic expansion of the heat flux near the ends of the crack are obtained in closed form.

[1] Birman V., Byrd L. W., “Modeling and analysis of functionally graded materials and structures”, ASME Appl. Mech. Rev., 60 (2007), 195–216

[2] Parton V. Z., Mekhanika razrusheniya, Nauka, M., 1990 | MR

[3] Sladek J., Sladek V., Zhan Ch., “An advanced numerical method for computing elastodynamic fracture parameters in functionally graded materials”, Computat. Materials Sci., 32 (2005), 532–543

[4] Chan Youn-Sha, Gray L. J., Kaplan T., Paulino G. H., “Green's function for a two-dimensional exponentially graded elastic medium”, Proc. R. Soc. Lond. A, 460 (2004), 1689–1706 | MR | Zbl

[5] Chkadua O., Mikhailov S. E., Natroshvili D., “Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. II: Solution regularity and asymptotics”, J. Integral Equations and Applications, 22:1 (2010), 19–37 | MR | Zbl

[6] Glushko A. V., Loginova E. A., “Asimptoticheskie svoistva resheniya zadachi o statsionarnom raspredelenii tepla v neodnorodnoi ploskosti s treschinoi”, Vestnik Voronezhskogo gos. un-ta. Ser.: Fizika i Matematika, 2010, no. 2, 47–50

[7] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976

[8] Vladimirov V. S., Mikhailov V. P., Vasharin A. A. i dr., Sbornik zadach po uravneniyam matematicheskoi fiziki, Nauka, M., 1982

[9] Vatson G. N., Teoriya besselevykh funktsii, Izd-vo inostr. lit.-ry, M., 1949

[10] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | MR