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Well-posed Boundary Value Problems for New Classes of Singular Integral Equations in Cylindrical Domains

  • Nusrat RajabovEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)

Abstract

In this work a class of three-dimensional complex integral equation in cylindrical domains is investigated in the case when the lateral surface may have singularity or super-singularity. For this type of integral equations condition for kernels are found under which the problem of finding solution is reduced to the problem of finding two splitting systems of integral equations which can be treated by existing methods. In this case the solution are obtained in an explicit form. In the case of more general kernels the, inversion formula is found in terms of the values on the surface of the cylinder. In model cases the solution of the integral equation is found in the form of absolutely and uniformly convergent generalised power series in powers of \((t-a)\) and the inversion formula is presented. It is used to investigate further Dirichlet-type boundary problems.

Keywords

Boundary value problems Integral equations Well-posedness problems 

Notes

Acknowledgement

The author is grateful to Professor Michael Ruzhansky for discussions and remarks about the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Research Institute of the Tajik National UniversityDushanbeTajikistan

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