Mixed Problem for Laplace’s Equation in an Arbitrary Circular Multiply Connected Domain

2018 ◽  
pp. 135-152 ◽  
Author(s):  
Vladimir Mityushev
Keyword(s):  
Mixed Problem ◽  
Connected Domain ◽  
Laplace’S Equation ◽  
Multiply Connected Domain ◽  
Laplace's Equation ◽  
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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