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
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Аннотация
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.
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Показатели — AkademScholar · Скоро