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The Bitsadze–Samarskii Type Problem for Mixed Type Equation in the Domain with the Deviation from the Characteristics
- Source :
- Lobachevskii Journal of Mathematics. 41:1021-1030
- Publication Year :
- 2020
- Publisher :
- Pleiades Publishing Ltd, 2020.
-
Abstract
- For a mixed elliptic-hyperbolic type equation in a mixed domain, when the elliptic part is a sector of the circle, and the hyperbolic part consists of two characteristic triangles, the Bitsadze–Samarskii type nonlocal problem is investigated. A feature of such problems is that the boundary conditions in the hyperbolic parts of the boundary are determined by a first-order differential operator and pointwise link the values of the partial derivatives of the desired solution on the characteristics with the partial derivatives on arbitrary monotone curves lying inside the characteristic triangles of the equation. To solve the problem, the methods of the theory of partial differential equations and the theory of singular integral equations as well as the methods of energy integrals and complex analysis were used, with the help of which the existence and uniqueness theorem for the solution of the investigated problem is proved. Also, a method of reducing the investigated problem to an equivalent system of singular integral equations is shown, also, a method for solving this system is proposed, which allows to obtain a solution to the problem in explicit form.
- Subjects :
- Pointwise
Partial differential equation
Picard–Lindelöf theorem
General Mathematics
010102 general mathematics
Mathematical analysis
Boundary (topology)
Singular integral
Differential operator
01 natural sciences
Domain (mathematical analysis)
010305 fluids & plasmas
0103 physical sciences
Boundary value problem
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 18189962 and 19950802
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Lobachevskii Journal of Mathematics
- Accession number :
- edsair.doi...........0e820dfe6552d0f584ede2549fcb082a