The Dirichlet problem for the generalized bi-axially symmetric Helmholtz equation

2014/01/21 by M. S. Salakhitdinov, Salakhitdinov, M. S., Anvar Hasanov +1
Mathematics · Physics and Astronomy · #35A08 #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1401.5144

openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in R₂^ + = \ ( x,y ):x > 0,y > 0 \. They contain Kummer's confluent hypergeometric functions in three variables. In this paper, using one of the constructed fundamental solutions, the Dirichlet problem is solved in the domain Ω⊂ R₂^ +. Using the method of Green's functions, solution of this problem is found in an explicit form.

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