A method of Fourier series for solution of problems in piecewise inhomogeneous domains with rectilinear crack (screen)
Pleiades Publishing Ltd - 2008
Tóm tắt
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.
Từ khóa
Tài liệu tham khảo
I. M. Abdurakhmanov and M. G. Alishaev, “Plane Stationary Filtration in a Stratum Divided by a Straight Crack,” Izv. AN SSSR, Ser. Mekh. Zhidkosti Gaza, No. 4, 173–177 (1973).
I. B. Simonenko, “Electrostatics Problems in for Nonhomogenious Medium: The Case of a Thin Dielectric with a Large Dielectric Constant,” Differ. Uravn. 10, 301–309 (1974).
B. A. Vasil’ev, “Plane Stationary Heat Conduction Problem for a Composite Wedge-shaped Domain,” Differ. Uravn. 20, 530–533 (1984).
A. V. Gurevich, A. L. Krylov, and D. N. Topor, “Solution of Plane Problems in the Hydrodynamics of Porous Media in the Vicinity of Discontinuities Using the Complex Potential Method,” Dokl. Akad. Nauk SSSR 298, 846–850 (1988).
V. V. Murzenko, “Analytical Solutions of Problems about the Stationary Flow of Fluids in Strata with Hydrodiscontinuity Cracks,” Izv. Ross. Akad. Nauk, Mekh. Zhidkosti Gaza, No. 2, 74–82 (1994).
A. V. Setukha, “On the Three-Dimensional Neumann Boundary Value Problem with a Generalized Boundary Condition in a Domain with Smooth Closed Boundary,” Differ. Uravn. 41, 1177–1189 (2005) [Differ. Equations 41, 1237–1252 (2005)].
S. K. Godunov, Equations of Mathematical Physics (Nauka, Moscow, 1971) [in Russian].
A. S. Kholodovskii and S. E. Kholodovskii, “Fourier Quasi-Integral Expansions of Functions and Their Applications to the Solution of Boundary Value Problems,” Differ. Uravn. 40, 1412–1416 (2004) [Differ. Equations 40, 1491–1495 (2004)].
O. V. Golubeva, “A Generalization of the Circle Theorem to Filtration Flows,” Izv. AN SSSR, Ser. Mekh. Zhidkosti Gaza, No. 1, 113–116 (1966).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions, (Nauka, Moscow, 1981) [in Russian].