Dirichlet problem for axisymmetric potential fields in a disk of the meridian plane. I

Springer Science and Business Media LLC - Tập 52 - Trang 564-585 - 2000
S. A. Plaksa1
1Institute of Mathematics, Ukranian Academy of Sciences, kiev

Tóm tắt

We develop new methods for the solution of boundary-value problems in the meridian plane of an antisymmetric potential solenoidal field with regard for the nature and specific features of axisymmetric problems. We determine the solutions of the Dirichlet problems for an axisymmetric potential and the Stokes flow function in a disk in an explicit form.

Tài liệu tham khảo

M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models [in Russian] Nauka, Moscow 1977.

V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 2, Nauka. Moscow (1974).

V. I. Smimov, A Course in Higher Mathematics [in Russian], Vol. 3, Part 2, Nauka, Moscow (1969).

V. I. Smirnov, A Course in Higher Mathematics [in Russian], Vol. 4, Gostekhizdat, Moscow (1951).

C. Miranda, Partial Differential Equations of Elliptic Type [Russian translation] Inostrannaya Literatura, Moscow 1957.

S. G. Mikhlin, Linear Partial Differential Equations [in Russian] Vysshaya Shkola, Moscow 1977.

M. Brelot, Elements de la Theorie Classique du Potentiel [Russian translation] Mir, Moscow 1964.

L. G. Mikhailov and N. Radzhabov, “An analog of the Poisson formula for certain second-order equations with singular line,” Dokl. Akad. Nauk Tadzh. SSR, 15, No. 11, 6–9 (1972).

N. Radzhabov, “Construction of potentials and investigation of inner and outer boundary-value problems of Dirichlet and Neumann types for the Euler-Poisson-Darboux equations on a plane,” Dokl. Akad. Nauk Tadzh. SSR, 17, No. 8, 7–11 (1974).

L. G. Loitsyanskii, Mechanics of Liquids and Gases [in Russian] Nauka, Moscow 1987.

J. K. Batchelor, An Introduction to Fluid Dynamics [Russian translation] Mir, Moscow 1973.

N. Radzhabov. “Boundary-value problems for an equation of axisymmetric field theory,” in: Investigations of Boundary-Value Problems in the Theory of Functions and Differential Equations [in Russian], Academy of Sciences of Tadzhik SSR, Dushanbe (1965), pp. 79–128.