Abstract:
The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent'ev–Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze's terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex.
\Bibitem{Sol12}
\by A.~P.~Soldatov
\paper On Dirichlet-type problems for the Lavrent'ev--Bitsadze equation
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 278
\pages 242--249
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3402}
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\elib{https://elibrary.ru/item.asp?id=17928427}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 278
\pages 233--240
\crossref{https://doi.org/10.1134/S0081543812060223}
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This publication is cited in the following 6 articles:
Tursun K. Yuldashev, Farhod D. Rakhmonov, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 060004
Yuldashev T.K., “Nonlocal Inverse Problem For a Pseudohyperbolic-Pseudoelliptic Type Integro-Differential Equations”, Axioms, 9:2 (2020), 45
A. V. Kopaev, “Oblique Derivative Problem Solution for the Lavrentyev-Bitsadze Equation in a Half-Plane”, Mat. mat. model., 2019, no. 6, 1
O. D. Algazin, “Polynomial Solutions of the Dirichlet Problem for the Tricomi Equation in a Strip”, Mat. mat. model., 2018, no. 3, 1
O. Kh. Masaeva, “Uniqueness of solutions to Dirichlet problems for generalized Lavrent'ev–Bitsadze equations with a fractional derivative”, Electron. J. Differ. Equ., 2017, 74
A. P. Soldatov, “Mixed problems for the Lavrent'ev–Bitsadze equation”, Applications of Mathematics in Engineering and Economics (AMEE `12), AIP Conf. Proc., 1497, eds. V. Pasheva, G. Venkov, Amer. Inst. Phys., 2012, 199–204