Explicit solution of differential boundary value problems such as the Riemann problem
https://doi.org/10.67268/1812-5093-2026-34-1-56-67
EDN: FEQFZF
Abstract
Generalized Riemann boundary problems are studied on a closed curve located on the complex plane. The boundary condition of the problems, along with the limit values of the desired functions, includes the limit values of their derivatives. The boundary conditions is written using determinants close to Vronsky's determinants. The solution of the problems is reduced to solving the classical Riemann problem and solving linear differential equations in areas of the complex plane with some restrictions on the solutions. The conditions for the solvability of the initial problems are indicated explicitly, and when they are fulfilled, explicit formulas for solutions are indicated. Examples are given.
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Review
For citations:
Shilin A.P. Explicit solution of differential boundary value problems such as the Riemann problem. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):56-67. (In Russ.) https://doi.org/10.67268/1812-5093-2026-34-1-56-67. EDN: FEQFZF
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