Fundamental solutions of a class of degenerate elliptic equation
Baishemirov Z. Berdyshev A. Hasanov A.
August 2023John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2023#46Issue 1213103 - 13109 pp.
In this paper, for the elliptic equation with two lines of different order of degeneration, given in the first quarter of the plane (Figure presented.), four fundamental solutions are constructed that are expressed by Appells hypergeometric functions (Figure presented.) of two variables. By means the decomposition formula of the Appells function in products of the Gauss hypergeometric function, it is proved that the constructed fundamental solutions possess a logarithmic singularity for (Figure presented.).
degenerate elliptic equation , fundamental solutions , Greens functions , hypergeometric function , logarithmic singularity
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Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty, 050012, Kazakhstan
Institute of Information and Computational Technologies, Almaty, 050010, Kazakhstan
School of Applied Mathematics, Kazakh-British Technical University, Almaty, 050010, Kazakhstan
Institute of Mathematics, Uzbek Academy of Sciences, Tashkent, 100170, Uzbekistan
Institute of Mathematics
Institute of Information and Computational Technologies
School of Applied Mathematics
Institute of Mathematics
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