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- Title
Gellerstedt problem with nonclassical matching conditions for the solution gradient on the type change line with data on internal characteristics.
- Authors
Moiseev, T.
- Abstract
We study the solvability of the Gellerstedt problem for the Lavrent'ev-Bitsadze equation. An initial function is posed in the ellipticity domain of the equation on the boundary of the unit half-circle with center the origin. Zero conditions are posed on characteristics in the hyperbolicity domain of the equation. 'Frankl-type conditions' are posed on the type change line of the equation. We show that the problem is either conditionally solvable or uniquely solvable. We obtain a closed-form solvability condition in the case of conditional solvability. We derive integral representations of the solution in all cases.
- Subjects
NONCLASSICAL mathematical logic; HILBERT'S tenth problem; BOUNDARY value problems; INTEGRALS; MATHEMATICAL analysis
- Publication
Differential Equations, 2016, Vol 52, Issue 8, p1023
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266116080073