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- W4285366838 abstract "A commutative algebra $mathbb{B}$ over the complex field with a basis $% {e_{1},e_{2}}$ satisfying the conditions $(e_{1}^{2}+e_{2}^{2})^{2}=0$, $% e_{1}^{2}+e_{2}^{2}neq 0$ is considered. This algebra is associated with the 2-D biharmonic equation. We consider Schwartz-type boundary-value problems on finding a monogenic function of the type $Phi (xe_{1}+ye_{2})=U_{1}(x,y),e_{1}+U_{2}(x,y),ie_{1}+U_{3}(x,y)% ,e_{2}+U_{4}(x,y),ie_{2}$, $(x,y)in D$, when the values of two components---either $U_{1}$, $U_{3}$ or $U_{1}$, $U_{4}$---are given on the boundary of a domain $D$ lying in the Cartesian plane $xOy$. For solving those boundary-value problems for a half-plane and for a disk, we develop methods that are based on solution expressions via Schwartz-type integrals and obtain solutions in the explicit form." @default.
- W4285366838 created "2022-07-14" @default.
- W4285366838 creator A5042482479 @default.
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- W4285366838 date "2021-09-09" @default.
- W4285366838 modified "2023-09-26" @default.
- W4285366838 title "Schwartz-type boundary-value problems for canonical domains in a biharmonic plane" @default.
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- W4285366838 doi "https://doi.org/10.37069/1810-3200-2021-18-3-4" @default.
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