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- Title
Gellerstedt problem with a generalized Frankl matching condition on the type change line with data on external characteristics.
- Authors
Moiseev, T.
- Abstract
We study the solvability of the Gellerstedt problem for the Lavrent'ev-Bitsadze equation with nonclassical matching conditions for the gradient of the solution (in the sense of Frankl) on the type change line of the equation. We prove that the inhomogeneous Gellerstedt problem with data on the external characteristics of the equation is solvable either uniquely or modulo a nontrivial solution of the homogeneous problem. We obtain integral representations of the solution of the problem in both the elliptic and the hyperbolic parts of the domain. The solution proves to be regular.
- Subjects
NONCLASSICAL mathematical logic; HYPERBOLIC functions; ELLIPTIC functions; HYPERGRAPHS; GRAPH theory
- Publication
Differential Equations, 2016, Vol 52, Issue 2, p240
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266116020099