RT Journal Article
T1 On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation
A1 Berdyshev, Abdumauvlen S.
A1 Cabada Fernández, Alberto
A1 Karimov, Erkinjon T.
K1 Transmitting condition
K1 Parabolic-hyperbolic equation
K1 Green’s function
AB In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problem
PB MDPI
YR 2020
FD 2020
LK http://hdl.handle.net/10347/23638
UL http://hdl.handle.net/10347/23638
LA eng
NO Berdyshev, A.; Cabada, A.; Karimov, E. On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation. Mathematics 2020, 8, 1030
NO The research of the first author is supported by the grant of the Committee of Sciences, Ministry of Education and Science of the Republic of Kazakhstan to the Institute of Information and Computational Technologies, project AP05131026. Second author is supported by the Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDER and by Xunta de Galicia, project ED431C 2019/02 (Spain)
DS Minerva
RD 25 abr 2026