Abstract:
We study the first boundary value problem for the elliptic-hyperbolic type equation with two perpendicular lines of change of type and spectral parameter. We prove the existence and uniqueness of the solution. In the proof of the uniqueness of solution we use the completeness of biorthogonal system in space L2. When building a solution as the sum of a series there is a problem of small denominators. We obtained estimates of the denominators of the separation from zero.
Keywords:
mixed type equation, Dirichlet problem, uniqueness, existence of a solution, spectral method.
Citation:
A. A. Gimaltdinova, “The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 634–649
\Bibitem{Gim15}
\by A.~A.~Gimaltdinova
\paper The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 634--649
\mathnet{http://mi.mathnet.ru/vsgtu1384}
\crossref{https://doi.org/10.14498/vsgtu1384}
\zmath{https://zbmath.org/?q=an:06969183}
\elib{https://elibrary.ru/item.asp?id=25687492}
Linking options:
https://www.mathnet.ru/eng/vsgtu1384
https://www.mathnet.ru/eng/vsgtu/v219/i4/p634
This publication is cited in the following 3 articles:
Kh. R. Rasulov, “Analog zadachi Trikomi dlya kvazilineinogo uravneniya smeshannogo tipa s dvumya liniyami vyrozhdeniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:4 (2022), 630–649
A. Gimaltdinova, “The Dirichlet problem for an equation of mixed type with two internal lines of type change”, Lobachevskii J. Math., 41:11, SI (2020), 2155–2167
K. S. Fayazov, Ya. K. Khudayberganov, “Ill-Posed Boundary Value Problem For Mixed Type System Equations With Two Degenerate Lines”, Sib. Electron. Math. Rep., 17 (2020), 647–659
Citation in format AMSBIB
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