Two linear conjugation problems, arising in the theory of the flow over an obstacle

Evgeny V Semenko (1) , Tatiana I Semenko (1)

1 Novosibirsk State Technical University

The tho linear conjugation problems on the real axis are considered. These problems additionally include the symmetry condition and the asymptotic condition at the infinity and arise in the hydrodynamics, in some models of the flow over an obstacle. The coefficients and right hand sides of the conjugation conditions (and, naturally, the solution) depend on the complex parameter (ω in the text). The specific feature of these problems is that the right hand sides of conjugation conditions include the values of the sought analytic functions in given points. Additionally the right hand side in the first problem includes the unknown function, that should be determined together with the solution. The solutions of the problems are constructed and some their properties are discussed, in particular the asymptotics of the solutions, when the parameter ω tends to zero, is found.

Mots clés: Linear conjugation problem; complex variables; analytic function; Cauchy integral

Domaines: Mathématiques [math]

Evgeny V Semenko, Tatiana I Semenko. Two linear conjugation problems, arising in the theory of the flow over an obstacle. 2021. ⟨hal-03234836⟩