Fundamental solutions of a class of degenerate elliptic equation

In this paper, for the elliptic equation with two lines of different order of degeneration, given in the first quarter of the plane (x,y)$$ \left(x,y\right) $$, four fundamental solutions are constructed that are expressed by Appell's hypergeometric functions F2$$ {F}_2 $$ of two variables. By...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-08, Vol.46 (12), p.13103-13109
Main Authors: Baishemirov, Zharasbek, Berdyshev, Abdumauvlen, Hasanov, Anvar
Format: Article
Language:English
Subjects:
degenerate elliptic equation
Degeneration
fundamental solutions
Green's functions
hypergeometric function
Hypergeometric functions
logarithmic singularity
Mathematical analysis
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, for the elliptic equation with two lines of different order of degeneration, given in the first quarter of the plane (x,y)$$ \left(x,y\right) $$, four fundamental solutions are constructed that are expressed by Appell's hypergeometric functions F2$$ {F}_2 $$ of two variables. By means the decomposition formula of the Appell's function in products of the Gauss hypergeometric function, it is proved that the constructed fundamental solutions possess a logarithmic singularity for r→0$$ r\to 0 $$.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9236