On a Volterra equation of the second kind with ‘incompressible’ kernel

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dc.contributor.author Jenaliyev, M.
dc.contributor.author Amangaliyeva, M.
dc.contributor.author Kosmakova, M.
dc.contributor.author Ramazanov, M.
dc.date.accessioned 2018-01-29T10:28:39Z
dc.date.available 2018-01-29T10:28:39Z
dc.date.issued 2015-12
dc.identifier.citation On a Volterra equation of the second kind with ‘incompressible’ kernel/M. Jenaliyev[a.o.]/Advances in Difference Equations.-2015 ru_RU
dc.identifier.issn 1687-1847
dc.identifier.uri http://rep.ksu.kz/handle/data/2156
dc.description.abstract Solving the boundary value problems of the heat equation in noncylindrical domains degenerating at the initial moment leads to the necessity of research of the singular Volterra integral equations of the second kind, when the norm of the integral operator is equal to 1. The paper deals with the singular Volterra integral equation of the second kind, to which by virtue of ‘the incompressibility’ of the kernel the classical method of successive approximations is not applicable. It is shown that the corresponding homogeneous equation when |λ| > 1 has a continuous spectrum, and the multiplicity of the characteristic numbers increases depending on the growth of the modulus of the spectral parameter |λ|. By the Carleman-Vekua regularization method (Vekua in Generalized Analytic Functions, 1988) the initial equation is reduced to the Abel equation. The eigenfunctions of the equation are found explicitly. Similar integral equations also arise in the study of spectral-loaded heat equations (Amangaliyeva et al. in Differ. Equ. 47(2):231-243, 2011). ru_RU
dc.language.iso en ru_RU
dc.publisher Springer International Publishing ru_RU
dc.relation.ispartofseries Advances in Difference Equations;
dc.subject Volterra integral equation ru_RU
dc.subject Abel equation ru_RU
dc.subject spectrum ru_RU
dc.subject nontrivial solution ru_RU
dc.subject characteristic equation ru_RU
dc.subject Carleman-Vekua regularization method ru_RU
dc.title On a Volterra equation of the second kind with ‘incompressible’ kernel ru_RU
dc.type Article ru_RU

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