Abstract:
We find the eigenvalues and eigenfunctions for the spectral Tricomi problem for an equation of mixed type with two lines of degeneracy and solve the planar and spatial Tricomi problems for equations with the Lavrent'ev–Bitsadze operator.
Citation:
K. B. Sabitov, A. A. Karamova, “Spectral properties of solutions of the Tricomi problem for equations of mixed type with two lines of degeneracy, and their applications”, Izv. Math., 65:4 (2001), 769–785
\Bibitem{SabGim01}
\by K.~B.~Sabitov, A.~A.~Karamova
\paper Spectral properties of solutions of the Tricomi problem for equations of mixed type with two lines of degeneracy, and their applications
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 769--785
\mathnet{http://mi.mathnet.ru/eng/im351}
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000351}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1857714}
\zmath{https://zbmath.org/?q=an:1038.35041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746856526}
Linking options:
https://www.mathnet.ru/eng/im351
https://doi.org/10.1070/IM2001v065n04ABEH000351
https://www.mathnet.ru/eng/im/v65/i4/p133
This publication is cited in the following 9 articles:
A. K. Urinov, K. T. Karimov, “Zadacha Trikomi — Neimana dlya trekhmernogo uravneniya smeshannogo tipa s singulyarnymi koeffitsientami”, Vladikavk. matem. zhurn., 25:4 (2023), 120–134
A. K. Urinov, K. T. Karimov, “The Third Boundary Problem for a Mixed-Type Equation with Three Singular Coefficients”, Lobachevskii J Math, 44:8 (2023), 3582
“APPROXIMATE SOLUTION OF AN INITIAL-BOUNDARY VALUE PROBLEM FOR AN NONHOMOGENEOUS SECOND-ORDER DIFFERENTIAL EQUATION OF MIXED TYPE WITH TWO DEGENERATE LINES”, Central Asian Problems of Modern Science and Education, 2020, 81
I. T. Tozhiboev, “Kraevye zadachi v spetsialnoi oblasti dlya uravneniya smeshannogo tipa”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 56, 17–28
K. T. Karimov, “Spektralnye zadachi dlya trekhmernykh ellipticheskikh uravnenii s singulyarnymi koeffitsientami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2017, no. 2(18), 7–19
Sabitov K.B., Gimaltdinova A.A., “On the Uniqueness of the Solution of the Tricomi Problem For the Lavrent'Ev-Bitsadze Equation With Complex Parameter and With Two Lines of Type Change”, Differ. Equ., 50:12 (2014), 1609–1624
N. V. Shustrova, “Obobschennaya zadacha Moravets dlya uravneniya Lavrenteva–Bitsadze s parametrom”, Sib. elektron. matem. izv., 3 (2006), 106–114
K. B. Sabitov, S. L. Khasanova, “Spectral properties of a boundary value problem with a normal derivative in the boundary condition for equations of mixed type and their applications”, Russian Math. (Iz. VUZ), 47:6 (2003), 60–72
N. V. Chiganova, “The eigenvalue problem for an equation of mixed type with two lines of degeneracy”, Russian Math. (Iz. VUZ), 47:9 (2003), 63–69
Citation in format AMSBIB
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