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 Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 7, Pages 16–30 (Mi ivm8807)

A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a singular coefficient

Gulbakhor M. Mirsaburova

Chair of Differential Equations and Geometry, Termez State University, 43 F. Khodzhaev str., Termez, 190111 Republic of Uzbekistan

Abstract: We consider a generalized Tricomi equation with a singular coefficient. For this equation in a mixed domain we study the corresponding problem, where a part of the boundary characteristic is free of boundary conditions; the deficient Tricomi condition is equivalently substituted by a nonlocal Frankl condition on a segment of the degeneration line. We prove that the stated problem is well-posed.

Keywords: gluing condition, uniqueness of solution, Tricomi singular integral equation, isolated singularity of the first order, Wiener–Hopf equation, index, residue.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:7, 13–26

UDC: 517.956

Citation: Gulbakhor M. Mirsaburova, “A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a singular coefficient”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 7, 16–30; Russian Math. (Iz. VUZ), 57:7 (2013), 13–26

Citation in format AMSBIB
\Bibitem{Mir13} \by Gulbakhor~M.~Mirsaburova \paper A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a~singular coefficient \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2013 \issue 7 \pages 16--30 \mathnet{http://mi.mathnet.ru/ivm8807} \transl \jour Russian Math. (Iz. VUZ) \yr 2013 \vol 57 \issue 7 \pages 13--26 \crossref{https://doi.org/10.3103/S1066369X13070025} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84879759731} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. Mirsaburov, S. T. Chorieva, “On a problem with shift for degenerate equation of mixed type”, Russian Math. (Iz. VUZ), 59:4 (2015), 38–45
2. Mirsaburova G.M., “Problem With An Analog of the Frankl Condition on the Boundary Characteristic and General Transmission Conditions on the Degeneration Segment For a Class of Mixed Type Equations”, Differ. Equ., 55:12 (2019), 1598–1610
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