Article

On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation

Abdumauvlen BerdyshevKazakh National Pedagogical University Named after Abai, Almaty 050010, KazakhstanAlberto CabadaDepartamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Galicia, SpainErkinjon KarimovInstitute of Mathematics, Uzbekistan Academy of Sciences, Mirzo Ulugbek str., 81, Tashkent 100170, Uzbekistan

Mathematicsjournal2020en

ABI

Abstract

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.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Numerical methods in inverse problems

Identifiers

DOI: 10.3390/math8061030

Citations and references

Cited by 6 14 references

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