An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions

1995 ◽  
Vol 11 (4) ◽  
pp. 399-407 ◽  
Author(s):  
E. M. E. Zayed ◽  
S. F. M. Ibrahim
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Connected Domain ◽  
General Type ◽  
Multiply Connected Domain ◽  
Expansion Theorem ◽  
Multiply Connected

Construction of complex potentials for multiply connected domain

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pyotr N. Ivanshin
Keyword(s):  
Integral Equation ◽  
Analytic Function ◽  
Linear System ◽  
Unbounded Domain ◽  
Connected Domain ◽  
Complex Potential ◽  
Cauchy Integral ◽  
Multiply Connected Domain ◽  
Multiply Connected ◽  
Impermeable Boundary

AbstractThe method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential – an analytic function in an unbounded multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given 𝑛-connected unbounded domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and 𝑛 logarithmic summands. The method is easily computable.

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