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The Riemann–Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions

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We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann–Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the… Click to show full abstract

We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann–Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation condition in Fokas’ scheme.

Keywords: riemann hilbert; equation quarter; helmholtz equation; quarter plane; hilbert approach

Journal Title: Letters in Mathematical Physics
Year Published: 2017

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