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 role of the Sommerfeld radiation condition in Fokas’ scheme.
KeywordsHelmholtz equation Riemann–Hilbert problem Lax pair
Mathematics Subject Classification35J25 35Q15 31B20
This work was partially supported by the National Science Foundation (NSF) under Grant No. DMS-0203104, by the Russian Science Foundation Grant No.17-11-01126, and by a Grant of the London Mathematical Society. The authors are grateful to M. Lyalinov for very useful discussions.
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