
Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary
- Author
- Makhmud Sadybekov and Aishabibi Dukenbayeva
- Organization
- Abstract
- In the paper we consider a stationary diffusion problem described by the Poisson equation. The problem is considered in a model domain, chosen as a half disk. Classical Dirichlet boundary conditions are set on the arc of the circle. New nonlocal boundary conditions are set on the bottom base. The first condition means the equality of flows through opposite radii, and the second condition is the proportionality of distribution densities on these radii with a variable coefficient of proportionality. Uniqueness and existence of the classical solution to the problem are proved. An inverse problem for the solution to the Poisson equation and its right-hand part depending only on an angular variable are considered. As an additional condition we use the boundary overdetermination. Inverse problems to the Dirichlet and Neumann problems, and to problems with nonlocal conditions of the equality of flows through the opposite radii are considered. The well-posedness of the formulated inverse problems is proved.
- Keywords
- Applied Mathematics, Analysis, Numerical Analysis, Computational Mathematics, Poisson equation, Dirichlet problem, Neumann problem, nonlocal boundary conditions, inverse problem, boundary overdetermination, CAUCHY-PROBLEM, HELMHOLTZ-EQUATION, SOLVABILITY, FLUXES
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8665957
- MLA
- Sadybekov, Makhmud, and Aishabibi Dukenbayeva. “Direct and Inverse Problems for the Poisson Equation with Equality of Flows on a Part of the Boundary.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 64, no. 5, 2019, pp. 777–91, doi:10.1080/17476933.2018.1517340.
- APA
- Sadybekov, M., & Dukenbayeva, A. (2019). Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 64(5), 777–791. https://doi.org/10.1080/17476933.2018.1517340
- Chicago author-date
- Sadybekov, Makhmud, and Aishabibi Dukenbayeva. 2019. “Direct and Inverse Problems for the Poisson Equation with Equality of Flows on a Part of the Boundary.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 64 (5): 777–91. https://doi.org/10.1080/17476933.2018.1517340.
- Chicago author-date (all authors)
- Sadybekov, Makhmud, and Aishabibi Dukenbayeva. 2019. “Direct and Inverse Problems for the Poisson Equation with Equality of Flows on a Part of the Boundary.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 64 (5): 777–791. doi:10.1080/17476933.2018.1517340.
- Vancouver
- 1.Sadybekov M, Dukenbayeva A. Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 2019;64(5):777–91.
- IEEE
- [1]M. Sadybekov and A. Dukenbayeva, “Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 64, no. 5, pp. 777–791, 2019.
@article{8665957, abstract = {{In the paper we consider a stationary diffusion problem described by the Poisson equation. The problem is considered in a model domain, chosen as a half disk. Classical Dirichlet boundary conditions are set on the arc of the circle. New nonlocal boundary conditions are set on the bottom base. The first condition means the equality of flows through opposite radii, and the second condition is the proportionality of distribution densities on these radii with a variable coefficient of proportionality. Uniqueness and existence of the classical solution to the problem are proved. An inverse problem for the solution to the Poisson equation and its right-hand part depending only on an angular variable are considered. As an additional condition we use the boundary overdetermination. Inverse problems to the Dirichlet and Neumann problems, and to problems with nonlocal conditions of the equality of flows through the opposite radii are considered. The well-posedness of the formulated inverse problems is proved.}}, author = {{Sadybekov, Makhmud and Dukenbayeva, Aishabibi}}, issn = {{1747-6933}}, journal = {{COMPLEX VARIABLES AND ELLIPTIC EQUATIONS}}, keywords = {{Applied Mathematics,Analysis,Numerical Analysis,Computational Mathematics,Poisson equation,Dirichlet problem,Neumann problem,nonlocal boundary conditions,inverse problem,boundary overdetermination,CAUCHY-PROBLEM,HELMHOLTZ-EQUATION,SOLVABILITY,FLUXES}}, language = {{eng}}, number = {{5}}, pages = {{777--791}}, title = {{Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary}}, url = {{http://doi.org/10.1080/17476933.2018.1517340}}, volume = {{64}}, year = {{2019}}, }
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