Article
Article name On the Solution of Boundary Value Problems for the Laplace Equation in the Half-Plane with Unbounded Boundary Functions. The Method of Quasi-Integrals of Fourier
Authors Yefimova I.A. Candidate of Physics and Mathematics, hol47@yandex.ru
Bibliographic description
Section Scientific Research
UDK 517.956
DOI
Article type
Annotation The third boundary value problem in the half-plane with sufficiently smooth boundary function which at infinity is an arbitrary polynomial growth was considered. The solution of the problem is obtained in the form of quasi-integral Fourier with classical Fourier coefficients of the n-th derivative of the boundary function. The results allow solving boundary value problems with singular points at infinity.
Key words boundary value problems with unbounded boundary functions, method of quasi-integrals of Fourier.
Article information
References 1. Fikhtengol’ts G. M. Kurs differentsial’nogo i integral’nogo ischisleniya. T. 3. M.: Nauka, 1962. 656 s. 2. Kholodovskii S. E. О razlozhenii funktsii v kvaziintegraly Fur’e i ikh prilozhenii // Obozrenii prikladnoi i promyshlennoi matematiki. 2003. T. 10. Vyp. 1. S. 247-248. 3. Kholodovskii A. S. and Kholodovskii S. E. Fourier quasi-integral expansions of functions and their applications to the solution of boundary value problems // Differential Equations. 2004. Vol. 40. №. 10. P. 1491 1495.
Full articleOn the Solution of Boundary Value Problems for the Laplace Equation in the Half-Plane with Unbounded Boundary Functions. The Method of Quasi-Integrals of Fourier