Geodesic
A method of Fourier series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen)
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1209-1213 
S. E. Kholodovskii. A method of Fourier series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen). Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1209-1213. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a6/
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     title = {A~method of {Fourier} series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen)},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the framework of the theory of harmonic functions, potentials of steady state processes (heat conduction, filtration, or electrostatics) in the piecewise inhomogeneous plane separated by a rectilinear strongly permeable crack or by a weakly permeable screen into two half-planes with quadratic permeability functions are constructed. The motion is induced by given singular points of the potential (sources, sinks, etc.). Compact formulas that directly express potentials in these domains in terms of harmonic functions are obtained; the resulting functions map the set of harmonic functions to the set of potentials conserving the type of singularities.

[1] Abdurakhmanov I. M., Alishaev M. G., “Ploskaya statsionarnaya filtratsiya v plaste, razdelennom pryamolineinoi treschinoi”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1973, no. 4, 173–177

[2] Simonenko I. B., “Zadachi elektrostatiki v neodnorodnoi srede. Sluchai tonkogo dielektrika s bolshoi dielektricheskoi postoyannoi”, Differents. ur-niya, 10:2 (1974), 301–309 | MR | Zbl

[3] Vasilev B. A., “Ploskaya statsionarnaya zadacha teorii teploprovodnosti dlya sostavnoi klinovidnoi oblasti”, Differents. ur-niya, 20:3 (1984), 530–533 | MR

[4] Gurevich A. B., Krylov A. L., Topor D. N., “Reshenie ploskikh zadach gidrodinamiki poristykh sred vblizi razryvnykh narushenii metodom kompleksnogo potentsiala”, Dokl. AN SSSR, 298:4 (1988), 846–850 | MR | Zbl

[5] Murzenko V. V., “Analiticheskie resheniya zadach statsionarnogo techeniya zhidkosti v plastakh s treschinami gidrorazryva”, Izv. RAN. Mekhan. zhidkosti i gaza, 1994, no. 2, 74–82 | MR | Zbl

[6] Setukha A. B., “O trekhmernoi kraevoi zadache Neimana s obobschennym granichnym usloviem v oblasti s gladkoi zamknutoi granitsei”, Differents. ur-niya, 41:9 (2005), 1177–1189 | MR | Zbl

[7] Godunov S. K., Uravneniya matematicheskoi fiziki, Nauka, M., 1971 | MR

[8] Kholodovskii A. C., Kholodovskii S. E., “O razlozhenii funktsii v kvaziintegraly Fure i ikh prilozhenii k resheniyu kraevykh zadach”, Diferents. ur-niya, 40:10 (2004), 1412–1416 | MR

[9] Golubeva O. V., “Obobschenie teoremy ob okruzhnosti na filtratsionnye techeniya”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1966, no. 1, 113–116 | MR

[10] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981 | MR | Zbl